Showing 1–50 of 93 results for author: Zheng, Z

Simultaneous Heisenberg-Limited Multiparameter Metrology via Indefinite Evolution

Authors: Hang Xu, Tailong Xiao, Ze Zheng, Xiaoyang Deng, Jinfeng Zheng, Jingzheng Huang, Guihua Zeng

Abstract: Quantum metrology achieves Heisenberg-limited precision in single-parameter estimation, but its multiparameter extension is fundamentally constrained by both parameter-encoding and measurement incompatibility. Noncommuting signal generators may cause incompatible parameter-encoding, preventing the quantum Fisher information matrix from simultaneously achieving the Heisenberg scale for all paramete… ▽ More Quantum metrology achieves Heisenberg-limited precision in single-parameter estimation, but its multiparameter extension is fundamentally constrained by both parameter-encoding and measurement incompatibility. Noncommuting signal generators may cause incompatible parameter-encoding, preventing the quantum Fisher information matrix from simultaneously achieving the Heisenberg scale for all parameters. Due to incompatible optimal measurements, the classical Fisher information matrix represents the practical attainable precision. Here, we introduce a multiparameter metrology framework based on indefinite evolution (IE), in which different control operations and signal reversal are placed in a coherent superposition. For a single-qubit probe with mutually orthogonal signal generators, IE enables compatible parameter encoding and optimal measurement without the signal reversal. For parallel generators, where only signal reversal realized by its generator is available, IE can achieve the same performance. We further extend this mechanism to noisy, many-body, and high-dimensional probes, and establish general conditions for achieving the simultaneous Heisenberg-limit. In contrast, definite evolution cannot achieve the same performance under compatible optimal measurements, even when signal reversal is available. Our results identify IE as an operational resource for overcoming multiparameter incompatibility and open a route toward attainable Heisenberg-limited sensing in interferometric platforms. △ Less

Submitted 11 August, 2026; originally announced August 2026.

Neural QAOA$^{2}$: Differentiable Joint Graph Partitioning and Parameter Initialization for Quantum Combinatorial Optimization

Authors: Zubin Zheng, Jiahao Wu, Shengcai Liu

Abstract: The quantum approximate optimization algorithm (QAOA) holds promise for combinatorial optimization but is constrained by limited qubits. While divide-and-conquer frameworks like QAOA$^{2}$ address scalability by partitioning graphs into subgraphs, existing methods suffer from two fundamental limitations: i) misalignment between heuristic partitioning metrics and quantum optimization goals, and ii)… ▽ More The quantum approximate optimization algorithm (QAOA) holds promise for combinatorial optimization but is constrained by limited qubits. While divide-and-conquer frameworks like QAOA$^{2}$ address scalability by partitioning graphs into subgraphs, existing methods suffer from two fundamental limitations: i) misalignment between heuristic partitioning metrics and quantum optimization goals, and ii) topology-blind parameter initialization that leads to optimization cold starts. To bridge these gaps, we propose Neural QAOA$^{2}$, an end-to-end differentiable framework that jointly generates graph partitions and initial parameters. By integrating a generative evaluative network (GEN), our method utilizes a differentiable quantum evaluator as a high-fidelity performance surrogate to provide direct gradient guidance, enabling the joint generator to learn the intrinsic mapping from graph topology to high-quality partition and parameter configurations. Extensive experiments on 183 QUBO, Ising, and MaxCut instances (21 to 1000 variables) demonstrate that our gradient-driven approach broadly outperforms heuristic baselines, ranking first on 101 instances. It exhibits zero-shot generalization across out-of-distribution graph topologies and scales. △ Less

Submitted 13 May, 2026; originally announced May 2026.

Comments: Accepted to ICML 2026

Universal qutrit control in asymmetric-top molecules

Authors: Qian-Qian Hong, Zhi-Jian Zheng, Zhe-Jun Zhang, Xin-Xia Jian, Chuan-Cun Shu

Abstract: We present a theoretical framework for universal single-qutrit control in asymmetric-top molecules, advancing molecular quantum information processing. In this approach, the qutrit is encoded in three rotational eigenstates, with an auxiliary state providing independent phase control within the computational manifold. We explore an analytic protocol for arbitrary single-qutrit gates, combining dir… ▽ More We present a theoretical framework for universal single-qutrit control in asymmetric-top molecules, advancing molecular quantum information processing. In this approach, the qutrit is encoded in three rotational eigenstates, with an auxiliary state providing independent phase control within the computational manifold. We explore an analytic protocol for arbitrary single-qutrit gates, combining directly addressable SU(2) rotations with auxiliary-state-mediated phase operations. To support this, we derive a multilevel pulse-area theorem that provides an explicit analytic mapping between gate parameters and control fields, enabling systematic design of high-fidelity microwave pulse sequences. Numerical simulations with 1,2-propanediol confirm the robustness of our approach, achieving Walsh-Hadamard gates with minimal leakage from the computational subspace. We further examine four SU(2) decomposition strategies and find that phase-error sensitivity depends on the decomposition sequence, while amplitude errors propagate along specific coherence pathways. Our results establish asymmetric-top molecules as a viable platform for qutrit-based quantum operations and offer an analytical method for precise quantum control of complex multilevel systems. △ Less

Submitted 5 May, 2026; originally announced May 2026.

Learning quantum disentanglement scheduling from reduced states via modular hybrid policies

Authors: Y. -X. Xiao, J. -Z. Han, Z. Zheng, Z. -H. Zhang, M. Xue, J. Li, X. Lv

Abstract: Quantum control with restricted state access is central to near-term quantum devices, where full wave-function information is unavailable. We study this problem through multiqubit disentanglement scheduling from partial observations, where a controller receives only two-qubit reduced density matrices and selects which qubit pair to disentangle at each step. We introduce a modular hybrid quantum--c… ▽ More Quantum control with restricted state access is central to near-term quantum devices, where full wave-function information is unavailable. We study this problem through multiqubit disentanglement scheduling from partial observations, where a controller receives only two-qubit reduced density matrices and selects which qubit pair to disentangle at each step. We introduce a modular hybrid quantum--classical policy framework consisting of classical preprocessing, a parameterized quantum circuit as a compact nonlinear latent block, and classical postprocessing for pair-selection probabilities. Benchmarking 4-, 5-, and 6-qubit tasks, we find that preprocessing is the dominant factor governing performance under reduced-state observations, while the quantum module provides a conditional compact representation whose utility depends on the input features and model budget. We further identify a performance--efficiency trade-off across policy families and find that increasing circuit width is generally more useful than increasing depth. These results provide practical design principles for hybrid policies in reduced-information quantum control. △ Less

Submitted 30 April, 2026; originally announced April 2026.

Comments: 13 pages, 11 figures; Preliminary manuscript prepared for summer program applications

Efficient Quantum Fully Homomorphic Encryption

Authors: Fengxia Liu, Zixian Gong, Kun Tian, Yi Zhang, Zhiming Zheng, Maozhi Xu

Abstract: Quantum fully homomorphic encryption (QFHE) enables arbitrary quantum computations on encrypted data, but prior constructions require prohibitive quantum resources--specifically, O(lambda^2) EPR pairs per T-gate evaluation using the Barrington-based approach (DSS16). This paper introduces a unified framework achieving exponential improvement over the generic Barrington-based approach in program le… ▽ More Quantum fully homomorphic encryption (QFHE) enables arbitrary quantum computations on encrypted data, but prior constructions require prohibitive quantum resources--specifically, O(lambda^2) EPR pairs per T-gate evaluation using the Barrington-based approach (DSS16). This paper introduces a unified framework achieving exponential improvement over the generic Barrington-based approach in program length. The central innovation is a novel modular arithmetic program (MA-Program) tailored to learning with errors (LWE) decryption. We show that LWE decryption computes the inner product <sk,ct> mod q, a modular inner product that is NOT a symmetric function. Thus, prior symmetric-function optimizations (Sinha's O(n)-state branching programs) do not apply. Our MA-Program tracks partial sums modulus q with state space Z_q requiring O(log q) bits, yielding programs of state count O(lambda) with binary encoding O(log lambda) and length O(lambda log lambda). This reduces the quantum gadget size from O(lambda^2) to O(lambda log^2 lambda) EPR pairs. To achieve a fully classical client, we transfer all quantum resources (EPR preparation, Bell measurements, adaptive error correction) to the server via the MA-Program gadget framework. Clients only perform classical LWE key generation, Pauli key encryption under classical FHE, and no quantum operations; a layered key structure further eliminates circular security assumptions. For parallel computation, we adopt the MBQC framework with flow functions, supporting up to O(log lambda) parallel measurements per layer. This separates offline resource preparation from online adaptive measurement, enabling parallel processing while maintaining deterministic evaluation. △ Less

Submitted 21 June, 2026; v1 submitted 25 April, 2026; originally announced April 2026.

Comments: 32pages, 2figures

Simultaneous Detection of High-Dimensional Entanglement for Two Unknown Quantum States

Authors: Mao-Sheng Li, Chang-Yue Zhang, Zheng Zheng, Zhihua Chen, Zhen-Peng Xu, Zhihao Ma, Yan-Ling Wang, Shao-Ming Fei, Zhu-Jun Zheng, Otfried Gühne

Abstract: The state overlap, quantified via $\tr[ρσ]$, is a metric widely used to assess the closeness between two quantum states $ρ$ and $σ$. Although global state overlap alone does not directly capture entanglement properties, we uncover that incorporating local state overlaps provide profound insights into the entanglement characteristics of quantum states. To be precise, the ratio of global to local st… ▽ More The state overlap, quantified via $\tr[ρσ]$, is a metric widely used to assess the closeness between two quantum states $ρ$ and $σ$. Although global state overlap alone does not directly capture entanglement properties, we uncover that incorporating local state overlaps provide profound insights into the entanglement characteristics of quantum states. To be precise, the ratio of global to local state overlaps provides a lower bound on the Schmidt number, which is usually used for quantifying high-dimensional entanglement. Unlike conventional methods for detecting entanglement, the approach here can simultaneously reveal entanglement information for two unknown quantum states. Moreover, state overlap can be efficiently determined through local randomized measurement methods, which ensures the experimental feasibility of our approach. In a special case, our criterion reduces to an entanglement criterion that is more powerful than the two criteria used most in experiment--the purity criterion and the fidelity-based criterion and also outperform the $p_3$-PPT method in specific instances. Our findings highlight a promising direction for advancements in entanglement detection experiments. △ Less

Submitted 21 March, 2026; originally announced March 2026.

Comments: 15 pages , 4 figures, comments are welcome!

Distribution of fidelity zeros in two-band topological models

Authors: Siyan Lin, Zhen-Yu Zheng, Shu Chen

Abstract: We investigate the distribution of fidelity zeros in two-band topological models by extending the phase transition driving parameter into the complex plane. Within the biorthogonal formulation, we unveil that fidelity zeros are related to momentum modes for which the real part of the energy gap vanishes. Guided by this relation, we analyze the Kitaev chain, the Haldane model, and the Qi-Wu-Zhang (… ▽ More We investigate the distribution of fidelity zeros in two-band topological models by extending the phase transition driving parameter into the complex plane. Within the biorthogonal formulation, we unveil that fidelity zeros are related to momentum modes for which the real part of the energy gap vanishes. Guided by this relation, we analyze the Kitaev chain, the Haldane model, and the Qi-Wu-Zhang (QWZ) model. In finite-size systems the zeros form discrete lines parallel to the imaginary axis, while in the thermodynamic limit they accumulate into extended regions in the complex parameter plane. For the Kitaev and Haldane models, the accessible interval of the real part of the complexified parameter is bounded by the critical points of the corresponding topological transitions. For the QWZ model, the transitions at $u = \pm2$ are identified in the same way, whereas the critical point at $u = 0$ is signaled by fidelity zeros crossing the real axis. These results extend the fidelity-zero framework to topological quantum phase transitions and clarify how critical information is encoded in complexified parameter space. △ Less

Submitted 19 March, 2026; originally announced March 2026.

Kirkwood-Dirac classical states based on discrete Fourier transform: Representation with directed graph

Authors: Lin-Yan Cai, Ying-Hui Yang, Zhu-Jun Zheng

Abstract: The Kirkwood-Dirac (KD) quasiprobability distribution is a fundamental representation for quantum states and has been widely applied in quantum metrology, quantum chaos, weak values in recent years. A quantum state is KD-classical if its KD-quasiprobability distribution forms a valid classical probability distribution with respect to two given bases, and KD-nonclassical otherwise, with the latter… ▽ More The Kirkwood-Dirac (KD) quasiprobability distribution is a fundamental representation for quantum states and has been widely applied in quantum metrology, quantum chaos, weak values in recent years. A quantum state is KD-classical if its KD-quasiprobability distribution forms a valid classical probability distribution with respect to two given bases, and KD-nonclassical otherwise, with the latter being closely associated with quantum advantages in various quantum processes. In this work, we investigate the structural characteristics of the KD-classical state set when the transition matrix between two orthonormal bases takes the form of a discrete Fourier transform (DFT) matrix. First, we adopt an alternative analytical approach to prove that the set of KD-classical states in a $p^r$-dimensional Hilbert space is the convex hull of KD-classical pure states--a conclusion that was recently established by De Bi{è}vre et al [Annales Henri Poincar{é}, 1-20, 2025]. Furthermore, we define a directed graph and use it to characterize KD-classical pure states in a Hilbert space of arbitrary dimension $d$. That is, the convex hull of KD-classical pure states along any path from the start vertex to the end vertex in this directed graph is exactly the intersection of the KD-classical state set and the linear space spanned by these path-associated KD-classical pure states. This general result not only yields the $p^r$-dimensional conclusion in a straightforward manner but also encompasses Theorem 2 in the existing work [J. Phys. A, 57, 435303, 2024], demonstrating its generality and inclusiveness. △ Less

Submitted 14 March, 2026; originally announced March 2026.

Comments: 30 pages

Microwave response of electrically driven spins in a three-qubit quantum processor

Authors: Tanner M. Janda, Heun Mo Yoo, Connor Nasseraddin, Adam R. Mills, Zhaoyi Joy Zheng, Jason R. Petta

Abstract: In electric dipole spin resonance (EDSR), a single spin is electrically driven in the field gradient produced by a micromagnet. While EDSR has enabled high fidelity gate operations in many devices, there are reports of unexpected non-linearities in the Rabi frequency as a function of microwave drive amplitude. We carefully measure the response of Loss-DiVincenzo (LD) single spin qubits to resonant… ▽ More In electric dipole spin resonance (EDSR), a single spin is electrically driven in the field gradient produced by a micromagnet. While EDSR has enabled high fidelity gate operations in many devices, there are reports of unexpected non-linearities in the Rabi frequency as a function of microwave drive amplitude. We carefully measure the response of Loss-DiVincenzo (LD) single spin qubits to resonant drives as well as simultaneous resonant and off-resonant drives, as would be encountered in a realistic quantum processor. With the microwave amplitude carefully calibrated, we find that the Rabi frequency scales linearly with drive amplitude, even when all three spins are driven simultaneously. We also determine that heating-induced resonance frequency shifts from off-resonant drives are comparable to typical temporal drifts. Our results indicate that the previously observed nonlinear response is not a general feature of LD spin qubits. △ Less

Submitted 9 March, 2026; originally announced March 2026.

Practical implementation of arbitrary nonlocal controlled-unitary gate via indefinite causal order

Authors: Wen-Qiang Liu, Zi-Han Zheng, Zhang-Qi Yin, Hai-Rui Wei

Abstract: Quantum gate teleportation enables the implementation of nonlocal quantum operations without direct interactions between distant nodes. We propose an efficient protocol for implementing arbitrary controlled-unitary (CU) gates acting on two spatially separated parties via indefinite causal order (ICO). By establishing a maximally entanglement between two remote nodes and coherently superposing orde… ▽ More Quantum gate teleportation enables the implementation of nonlocal quantum operations without direct interactions between distant nodes. We propose an efficient protocol for implementing arbitrary controlled-unitary (CU) gates acting on two spatially separated parties via indefinite causal order (ICO). By establishing a maximally entanglement between two remote nodes and coherently superposing orders of single-qubit gates, our protocol circumvents the drawback of complex local two-qubit operations. This ICO-based approach enables full programmability of CU gates by adjusting the inherent single-qubit operations, offering advantages over conventional fixed causal-order methods in terms of reduced circuit complexity and improved experimental flexibility. Furthermore, we develop an optical construction to implement the polarization CU gate using a stable and reciprocal Sagnac interferometer. Our work establishes a practical framework for scalable distributed quantum computation with flexible operations. △ Less

Submitted 9 March, 2026; originally announced March 2026.

Comments: 12 pages 3 figures

Journal ref: New Journal of Physics 28, 034506 (2026)

A Dynamical Lie-Algebraic Framework for Hamiltonian Engineering and Quantum Control

Authors: Yanying Liang, Ruibin Xu, Mao-Sheng Li, Haozhen Situ, Zhu-Jun Zheng

Abstract: Determining the unitary dynamics accessible from finite Hamiltonian resources is a central problem in Hamiltonian engineering and quantum control. Dynamical Lie algebras (DLAs) connect available control Hamiltonians with the reachable dynamics, but their use as a design tool for modifying Hamiltonian generator sets remains less developed. In this work, we develop a finite-dimensional DLA framework… ▽ More Determining the unitary dynamics accessible from finite Hamiltonian resources is a central problem in Hamiltonian engineering and quantum control. Dynamical Lie algebras (DLAs) connect available control Hamiltonians with the reachable dynamics, but their use as a design tool for modifying Hamiltonian generator sets remains less developed. In this work, we develop a finite-dimensional DLA framework for three generator-set operations: composition, invariance, and reduction. For composition, we construct direct sums of component DLAs using spectral projectors on an auxiliary register. For invariance, we analyze when modifications of Pauli-string generating sets preserve the generated Lie algebra, and introduce algebraic diagnostics for added generators. For reduction, we consider compact reductive DLAs and show how projection onto selected simple ideals gives reduced generating sets whose Lie closures are the corresponding ideal sums. We illustrate these results with finite-dimensional examples and numerical checks, including direct-sum dimension addition, central-spin invariance diagnostics, and DLA-based ansatz reduction for block-local Hamiltonians. The results show how DLA structure can be used to diagnose controllability and guide Hamiltonian generator design under explicit algebraic assumptions. △ Less

Submitted 19 July, 2026; v1 submitted 5 March, 2026; originally announced March 2026.

From Classical to Quantum Reinforcement Learning and Its Applications in Quantum Control: A Beginner's Tutorial

Authors: Abhijit Sen, Sonali Panda, Mahima Arya, Subhajit Patra, Zizhan Zheng, Denys I. Bondar

Abstract: This tutorial is designed to make reinforcement learning (RL) more accessible to undergraduate students by offering clear, example-driven explanations. It focuses on bridging the gap between RL theory and practical coding applications, addressing common challenges that students face when transitioning from conceptual understanding to implementation. Through hands-on examples and approachable expla… ▽ More This tutorial is designed to make reinforcement learning (RL) more accessible to undergraduate students by offering clear, example-driven explanations. It focuses on bridging the gap between RL theory and practical coding applications, addressing common challenges that students face when transitioning from conceptual understanding to implementation. Through hands-on examples and approachable explanations, the tutorial aims to equip students with the foundational skills needed to confidently apply RL techniques in real-world scenarios. △ Less

Submitted 20 July, 2026; v1 submitted 13 January, 2026; originally announced January 2026.

Noise-Resilient Heisenberg-limited Quantum Sensing via Indefinite-Causal-Order Error Correction

Authors: Hang Xu, Xiaoyang Deng, Ze Zheng, Tailong Xiao, Guihua Zeng

Abstract: Quantum resources can, in principle, enable Heisenberg-limited (HL) sensing, yet no-go theorems imply that HL scaling is generically unattainable in realistic noisy devices. While quantum error correction (QEC) can suppress noise, its use in quantum sensing is constrained by stringent requirements, including prior noise characterization, restrictive signal-noise compatibility conditions, and measu… ▽ More Quantum resources can, in principle, enable Heisenberg-limited (HL) sensing, yet no-go theorems imply that HL scaling is generically unattainable in realistic noisy devices. While quantum error correction (QEC) can suppress noise, its use in quantum sensing is constrained by stringent requirements, including prior noise characterization, restrictive signal-noise compatibility conditions, and measurement-based syndrome extraction with global control. Here we introduce an ICO-based QEC protocol, providing the first application of indefinite causal order (ICO) to QEC. By coherently placing auxiliary controls and noisy evolution in an indefinite causal order, the resulting noncommutative interference enables an auxiliary system to herald and correct errors in real time, thereby circumventing the limitations of conventional QEC and restoring HL scaling. We rigorously establish the protocol for single- and multi-noise scenarios and demonstrate its performance in single-qubit, many-body, and continuous-variable platforms. We further identify regimes in which error correction can be implemented entirely by unitary control, without measurements. Our results reveal ICO as a powerful resource for metrological QEC and provide a broadly applicable framework for noise-resilient quantum information processing. △ Less

Submitted 4 January, 2026; originally announced January 2026.

Comments: 4 figures

Achievable Trade-Off in Network Nonlocality Sharing

Authors: Ming-Xiao Li, Yuqi Li, Rui-Bin Xu, Mo-Ran Zhu, Haitao Ma, Chang-Yue Zhang, Zhu-Jun Zheng

Abstract: Quantum networks are essential for advancing scalable quantum information processing. Quantum nonlocality sharing provides a crucial strategy for the resource-efficient recycling of quantum correlations, offering a promising pathway toward scaling quantum networks. Despite its potential, the limited availability of resources introduces a fundamental trade-off between the number of sharable network… ▽ More Quantum networks are essential for advancing scalable quantum information processing. Quantum nonlocality sharing provides a crucial strategy for the resource-efficient recycling of quantum correlations, offering a promising pathway toward scaling quantum networks. Despite its potential, the limited availability of resources introduces a fundamental trade-off between the number of sharable network branches and the achievable sequential sharing rounds. The relationship between available entanglement and the sharing capacity remains largely unexplored, which constrains the efficient design and scalability of quantum networks. Here, we establish the entanglement threshold required to support unbounded sharing across an entire network by introducing a protocol based on probabilistic projective measurements. When resources fall below this threshold, we derive an achievable trade-off between the number of sharable branches and sharing rounds. To assess practical feasibility, we compare the detectability of our protocol with weak-measurement schemes and extend the sharing protocol to realistic noise models, providing a robust framework for nonlocality recycling in quantum networks. △ Less

Submitted 15 December, 2025; originally announced December 2025.

Comments: 16 pages, 6 figures

Emergence of long-range entanglement and odd-even effect in periodic generalized quantum cluster models

Authors: Zhen-Yu Zheng, Shu Chen

Abstract: We investigate the entanglement properties in a generalized quantum cluster model under periodic boundary condition. By evaluating the quantum conditional mutual information entropy under four subsystem partitions, we identify clear signatures of long-range entanglement. Specifically, when both the system size $N$ and the interaction range $m$ are odd, the system exhibits nonzero four-part quantum… ▽ More We investigate the entanglement properties in a generalized quantum cluster model under periodic boundary condition. By evaluating the quantum conditional mutual information entropy under four subsystem partitions, we identify clear signatures of long-range entanglement. Specifically, when both the system size $N$ and the interaction range $m$ are odd, the system exhibits nonzero four-part quantum conditional mutual information entropies in infinitesimal but finite field. This nonvanishing four-part quantum conditional mutual information entropy directly signals the presence of long-range entanglement. In contrast, all other combination of $N$ and $m$ yield vanishing four-part quantum conditional mutual information entropy. Remarkably, in the case of $N, m \in \text{odd}$, these long-range entangled features persist even in the presence of a large transverse field, demonstrating their robustness against quantum fluctuations. These results demonstrate how the interplay between system size and interaction range governs the emergence of long-range entanglement in one-dimensional generalized quantum cluster model. △ Less

Submitted 25 March, 2026; v1 submitted 15 December, 2025; originally announced December 2025.

Journal ref: Phys. Rev. B 113, 094446 (2026)

Many-Body Entanglement in Solid-State Emitters

Authors: Emma Daggett, Christian M. Lange, Bennet Windt, Arshag Danageozian, Alexander Senichev, Jordi Arnau Montañà-López, Chanchal, Kinjol Barua, Xingyu Gao, Zhaoyun Zheng, Vijin Kizhake Veetil, Souvik Biswas, Jonas M. Peterson, Na Liu, Chuchuan Hong, Teri Odom, Matthew Pelton, Tongcang Li, Jelena Vučković, Vladamir Shalaev, Alexandra Boltasseva, Sophia E. Economou, Jonathan D. Hood, Valentin Walther, Rahul Trivedi , et al. (1 additional authors not shown)

Abstract: The preparation and control of quantum states lie at the heart of quantum information science (QIS). Recent advances in solid-state quantum emitters (QEs) and nanophotonics have transformed the landscape of quantum photonic technologies, enabling scalable generation of quantum states of light and matter. A new frontier in solid-state quantum photonics is the engineering of many-body interactions b… ▽ More The preparation and control of quantum states lie at the heart of quantum information science (QIS). Recent advances in solid-state quantum emitters (QEs) and nanophotonics have transformed the landscape of quantum photonic technologies, enabling scalable generation of quantum states of light and matter. A new frontier in solid-state quantum photonics is the engineering of many-body interactions between QEs and photons to achieve robust coherence and controllable many-body entanglement. These entangled states, including photonic graph and cluster states, superradiant emission, and emergent quantum phases, are promising for quantum computation, sensing, and simulation. However, intrinsic inhomogeneities and decoherence in solid-state platforms pose significant challenges to realize such complex entangled states. This review provides an overview of the fundamental many-body interactions and dynamics at the light-matter interfaces of solid-state QEs, and discusses recent advances in mitigating decoherence and harnessing robust many-body coherence. △ Less

Submitted 25 November, 2025; originally announced November 2025.

Parameter Inference from Final-State Entanglement in Higgs Decays

Authors: Jia Liu, Masanori Tanaka, Xiao-Ping Wang, Jing-Jun Zhang, Zifan Zheng

Abstract: The decay out-states of unstable Standard Model (SM) particles provide a unique, well-defined intrinsic quantum-information probe of the SM parameter space. We use Higgs decays as a test case: after tracing out kinematics, we compute entanglement among final-state spins and colors across all decay channels and impose a near-maximal entanglement-entropy criterion. This criterion yields quantitative… ▽ More The decay out-states of unstable Standard Model (SM) particles provide a unique, well-defined intrinsic quantum-information probe of the SM parameter space. We use Higgs decays as a test case: after tracing out kinematics, we compute entanglement among final-state spins and colors across all decay channels and impose a near-maximal entanglement-entropy criterion. This criterion yields quantitative indications for fundamental parameters. Within the SM, the entanglement entropy exhibits a global maximum close to the observed Higgs mass and the measured $W$ mass, the latter being equivalent to the $SU(2)_L$ gauge coupling. In a two-parameter kappa framework, applying the same criterion points to an SM-like balance between vector and fermion couplings, constraining the ratio of the sector-wide rescalings. These results suggest that entanglement extremality can serve as a complementary handle on fundamental parameters. △ Less

Submitted 25 July, 2026; v1 submitted 21 November, 2025; originally announced November 2025.

Comments: 17 pages, 7 figures, accepted for publication in PRD

Report number: CPTNP-2025-042

Journal ref: Phys. Rev. D 114, 015036 (2026)

Bootstrapping Euclidean Two-point Correlators

Authors: Minjae Cho, Barak Gabai, Henry W. Lin, Jessica Yeh, Zechuan Zheng

Abstract: We develop a bootstrap approach to Euclidean two-point correlators, in the thermal or ground state of quantum mechanical systems. We formulate the problem of bounding the two-point correlator as a semidefinite programming problem, subject to the constraints of reflection positivity, the Heisenberg equations of motion, and the Kubo-Martin-Schwinger condition or ground-state positivity. In the dual… ▽ More We develop a bootstrap approach to Euclidean two-point correlators, in the thermal or ground state of quantum mechanical systems. We formulate the problem of bounding the two-point correlator as a semidefinite programming problem, subject to the constraints of reflection positivity, the Heisenberg equations of motion, and the Kubo-Martin-Schwinger condition or ground-state positivity. In the dual formulation, the Heisenberg equations of motion become "inequalities of motion" on the Lagrange multipliers that enforce the constraints. This enables us to derive rigorous bounds on continuous-time two-point correlators using a finite-dimensional semidefinite or polynomial matrix program. We illustrate this method by bootstrapping the two-point correlators of the ungauged one-matrix quantum mechanics, from which we extract the spectrum and matrix elements of the low-lying adjoint states. Along the way, we provide a new derivation of the energy-entropy balance inequality and establish a connection between the high-temperature two-point correlator bootstrap and the matrix integral bootstrap. △ Less

Submitted 29 June, 2026; v1 submitted 11 November, 2025; originally announced November 2025.

Comments: 54 pages, 17 figures; v2: improved numerics and added refs; v3: minor improvements

Real-time vacuum-state quantum random number generator on a chip

Authors: Guan-Ru Qiao, Bing Bai, Zi-Xuan Weng, Han-Shen Chen, Wei Zheng, Zhi-Yuan Zheng, You-Qi Nie, Jun Zhang, Jian-Wei Pan

Abstract: Quantum random number generators (QRNGs) produce true random numbers, which are guaranteed by the fundamental principles of quantum physics. Miniaturization of QRNGs is crucial for a wide range of communication and cryptography applications. Here, we first report a fully functional QRNG chip based on vacuum-state fluctuations, with dimensions of 16.6 mm x 7.8 mm. The quantum entropy source, which… ▽ More Quantum random number generators (QRNGs) produce true random numbers, which are guaranteed by the fundamental principles of quantum physics. Miniaturization of QRNGs is crucial for a wide range of communication and cryptography applications. Here, we first report a fully functional QRNG chip based on vacuum-state fluctuations, with dimensions of 16.6 mm x 7.8 mm. The quantum entropy source, which is achieved via hybrid photonic integration with a SiO2 waveguide, generates raw quantum random numbers. The hybrid photonic and electrical components are assembled into a compact ceramic package using system-in-package technology. A microcontroller unit acquires the raw data and outputs the processed quantum random numbers via a serial peripheral interface. According to the characterization results, the QRNG chip achieves a constant real-time output rate of 5.2 Mbps across the industrial temperature range of -40°C to 85°C, making it suitable for practical applications. △ Less

Submitted 16 September, 2025; originally announced September 2025.

Comments: 8 pages, 6 figures. Accepted by Physical Review Applied

Approximate universality and large measurement gain of Rabi model in a linear potential under strong Doppler broadening

Authors: Dongyang Yu, Zhan Zheng

Abstract: Harnessing quantum resources in the atomic external degrees of freedom, particularly matter-wave states with large momentum broadening, holds significant potential for enhancing the sensitivity of Kasevich-Chu atom gravimeters at the standard quantum limit. However, a fully quantum-mechanical investigation of the critical Doppler effect inherent to this approach remains lacking. Employing SU(2) Li… ▽ More Harnessing quantum resources in the atomic external degrees of freedom, particularly matter-wave states with large momentum broadening, holds significant potential for enhancing the sensitivity of Kasevich-Chu atom gravimeters at the standard quantum limit. However, a fully quantum-mechanical investigation of the critical Doppler effect inherent to this approach remains lacking. Employing SU(2) Lie group theory, we derive a generic scalar Riccati equation governing the unitary dynamics of the Rabi model within a linear potential and analyze the Doppler effect's impact on Rabi oscillations because of the strong coupling between the internal and external states. Furthermore, by integrating Fisher information theory, we demonstrate the approximate universality and high metrological gain of phase-rotation measurement protocols under strong Doppler broadening induced by large-momentum width. This theoretical work provides insightful implications for broader generalization, such as extensions to finite-temperature scenarios or multi-pulse sequences, exemplified by the $π/2-π-π/2$ pulse sequence characteristic of Kasevich-Chu atom gravimeters. Thus this study lays a theoretical foundation for developing high-sensitivity, noise-resistant atom gravimeters that leverage external-state quantum resources. △ Less

Submitted 28 August, 2025; v1 submitted 17 July, 2025; originally announced July 2025.

Comments: 4 Figures, 8 Pages, comments or suggestions are welcome

All-optical Raman control of ultracold atomic hyperfine states using pulsed jump protocol

Authors: Xin-Xia Jian, Zhi-Jian Zheng, Jun-Jie Jiang, Lin Zhou, Chuan-Cun Shu, Jun He

Abstract: We develop a pulse-driven jump protocol to achieve all-optical Raman control of ultracold atomic hyperfine states. By establishing general conditions for adiabatic evolution between quantum states in parameter space, we derive the essential pulse area and phase conditions necessary for quantum state transfer in a resonant single-$Λ$ three-level system. We extend this approach to a double-$Λ$ four-… ▽ More We develop a pulse-driven jump protocol to achieve all-optical Raman control of ultracold atomic hyperfine states. By establishing general conditions for adiabatic evolution between quantum states in parameter space, we derive the essential pulse area and phase conditions necessary for quantum state transfer in a resonant single-$Λ$ three-level system. We extend this approach to a double-$Λ$ four-level system by incorporating a neighboring intermediate state, which leads to a single-photon detuned $Λ$ three-level system. Through numerical simulations of the ultracold $^{87}$Rb atomic system, we demonstrate that high-fidelity and robust control of quantum state transfer can be achieved in the single-$Λ$ three-level system using stimulated Raman adiabatic passage (STIRAP) and the pulsed jump protocol. Furthermore, we show that the destructive quantum interference effects between resonant and detuned Raman pathways in the double-$Λ$ four-level system can be mitigated by optimizing the pulse area and two-photon detuning parameters within the pulsed jump protocol. This work presents a promising approach for achieving all-optical Raman control of quantum state transfer in ultracold atomic hyperfine states. △ Less

Submitted 14 April, 2025; originally announced April 2025.

Authenticated Sublinear Quantum Private Information Retrieval

Authors: Fengxia Liu, Zhiyong Zheng, Kun Tian, Yi Zhang, Heng Guo, Zhe Hu, Oleksiy Zhedanov, Zixian Gong

Abstract: This paper introduces a novel lower bound on communication complexity using quantum relative entropy and mutual information, refining previous classical entropy-based results. By leveraging Uhlmann's lemma and quantum Pinsker inequalities, the authors establish tighter bounds for information-theoretic security, demonstrating that quantum protocols inherently outperform classical counterparts in ba… ▽ More This paper introduces a novel lower bound on communication complexity using quantum relative entropy and mutual information, refining previous classical entropy-based results. By leveraging Uhlmann's lemma and quantum Pinsker inequalities, the authors establish tighter bounds for information-theoretic security, demonstrating that quantum protocols inherently outperform classical counterparts in balancing privacy and efficiency. Also explores symmetric Quantum Private Information Retrieval (QPIR) protocols that achieve sub-linear communication complexity while ensuring robustness against specious adversaries: A post-quantum cryptography based protocol that can be authenticated for the specious server; A ring-LWE-based protocol for post-quantum security in a single-server setting, ensuring robustness against quantum attacks; A multi-server protocol optimized for hardware practicality, reducing implementation overhead while maintaining sub-linear efficiency. These protocols address critical gaps in secure database queries, offering exponential communication improvements over classical linear-complexity methods. The work also analyzes security trade-offs under quantum specious adversaries, providing theoretical guarantees for privacy and correctness. △ Less

Submitted 26 July, 2025; v1 submitted 4 April, 2025; originally announced April 2025.

Loschmidt echo zeros in finite-size quantum systems with linear quench

Authors: Zhen-Yu Zheng, Xudong Liu, Siyan Lin, Yu Zhang, Shu Chen

Abstract: Dynamical quantum phase transitions reveal singularities in quench dynamics, characterized by the emergence of Loschmidt echo zeros at critical times, which usually exist only in the thermodynamic limit but are absent in finite-size quantum systems. In this Letter, we propose a theoretical scheme to probe Loschmidt echo zeros in finite-size systems by applying a two-step quenching protocol, which… ▽ More Dynamical quantum phase transitions reveal singularities in quench dynamics, characterized by the emergence of Loschmidt echo zeros at critical times, which usually exist only in the thermodynamic limit but are absent in finite-size quantum systems. In this Letter, we propose a theoretical scheme to probe Loschmidt echo zeros in finite-size systems by applying a two-step quenching protocol, which offers an experimentally feasible approach to study Loschmidt echo zeros. Using the transverse Ising model as a test bed, we identify that the exact Loschmidt echo zeros can be always accessed by tuning the quench rate, when the quench is across the phase transition point. The associated rate function displays divergence at critical times, accompanying with the change of the dynamical topological order parameter. The critical times are influenced by the quench rate, system size, and momentum modes, embodying the interplay between finite-size effects and critical dynamics. Moreover, the generality of these observations is further confirmed in the XY and Haldane models. △ Less

Submitted 6 January, 2026; v1 submitted 1 April, 2025; originally announced April 2025.

Journal ref: Phys. Rev. B 113, L020301 (2026)

The quantum non-Markovianity for a special class of generalized Weyl channel

Authors: Wen Xu, Mao-Sheng Li, Bo Li, Gui-Mei Jiao, Zhu-Jun Zheng

Abstract: A quantum channel is usually represented as a sum of Kraus operators. The recent study [Phys. Rev. A 98, 032328 (2018)] has shown that applying a perturbation to the Kraus operators in qubit Pauli channels, the dynamical maps exhibit interesting properties, such as non-Markovianity, singularity. This has sparked our interest in studying the properties of other quantum channels. In this work, we st… ▽ More A quantum channel is usually represented as a sum of Kraus operators. The recent study [Phys. Rev. A 98, 032328 (2018)] has shown that applying a perturbation to the Kraus operators in qubit Pauli channels, the dynamical maps exhibit interesting properties, such as non-Markovianity, singularity. This has sparked our interest in studying the properties of other quantum channels. In this work, we study a special class of generalized Weyl channel where the Kraus operators are proportional to the Weyl diagonal matrices and the rest are vanishing. We use the Choi matrix of intermediate map to study quantum non-Markovianity. The crossover point of the eigenvalues of Choi matrix is a singularity of the decoherence rates in the canonical form of the master equation. Moreover, we identify the non-Markovianity based on the methods of CP divisibility and distinguishability. We also quantify the non-Markovianity in terms of the Hall-Cresser-Li-Andersson (HCLA) measure and the Breuer-Laine-Piilo (BLP) measure, respectively. In particular, we choose mutually unbiased bases as a pair of orthogonal initial states to quantify the non-Markovianity based on the BLP measure. △ Less

Submitted 13 March, 2025; originally announced March 2025.

Comments: 21 pages,5 figures

Entangled mixed-state datasets generation by quantum machine learning

Authors: Ruibin Xu, Zheng Zheng, Yanying Liang, Zhu-Jun Zheng

Abstract: The advancement of classical machine learning is inherently linked to the establishment and progression of classical dataset. In quantum machine learning (QML), there is an analogous imperative for the development of quantum entangled datasets comprised with huge quantity and high quality. Especially for multipartite mixed-state datasets, due to the lack of suitable entanglement criteria, previous… ▽ More The advancement of classical machine learning is inherently linked to the establishment and progression of classical dataset. In quantum machine learning (QML), there is an analogous imperative for the development of quantum entangled datasets comprised with huge quantity and high quality. Especially for multipartite mixed-state datasets, due to the lack of suitable entanglement criteria, previous researchers often could only perform classification tasks on datasets extended based on Werner states or other well-structured states. This paper is dedicated to provide a method for generating mixed-state datasets for entangled-separable classification tasks. This method is based on supervised quantum machine learning and the concentratable entanglement measures. It furthers the assembly of quantum entangled datasets, inspires the discovery of new entanglement criteria with both classical and quantum machine learning, and provides a valuable resource for benchmarking QML models, thereby opening new avenues for exploring the rich structure of quantum entanglement in mixed states. Additionally, we benchmark several machine learning models using this dataset, offering guidance and suggestions for the selection of QML models. △ Less

Submitted 9 March, 2025; originally announced March 2025.

Comments: 25 pages,10 figures

Characterizing dynamical behaviors in topological open systems with boundary dissipations

Authors: Zhen-Yu Zheng, Xueliang Wang, Shu Chen

Abstract: We investigate the dynamics of the Su-Schrieffer-Heeger model with boundary dissipations described by Lindblad master equations and unravel distinct dynamical features in the topologically different phases of the underlying Hamiltonian. By examining the long-time damping dynamics, we uncover a dynamical duality phenomenon between the weak and strong dissipation region, which exists only in the top… ▽ More We investigate the dynamics of the Su-Schrieffer-Heeger model with boundary dissipations described by Lindblad master equations and unravel distinct dynamical features in the topologically different phases of the underlying Hamiltonian. By examining the long-time damping dynamics, we uncover a dynamical duality phenomenon between the weak and strong dissipation region, which exists only in the topologically non-trivial phase, linked to the structure of the Liouvillian spectra,particularly the stripe closest to the steady state. When dissipation is confined to a single boundary, the dynamical duality phenomenon still exists. Under this condition, the Liouvillian gap fulfills an exponential size scaling relation in the topologically non-trivial phase and a power-law size scaling relation in the topologically trivial phase. Within the topologically non-trivial region, we identify the existence of boundary-localized dark states in the thermodynamical limit, which is responsible for the exponential size decay of Liouvillian gap. △ Less

Submitted 26 December, 2025; v1 submitted 1 March, 2025; originally announced March 2025.

Journal ref: Phys. Rev. B 111, 214304 (2025)

Quantum state discrimination in a $\mathcal{PT}$-symmetric system of a single trapped ion

Authors: Chenhao Zhu, Tingting Shi, Liangyu Ding, Zhiyue Zheng, Xiang Zhang, Wei Zhang

Abstract: We experimentally demonstrate an unambiguous quantum state discrimination of two qubit states under a non-Hermitian Hamiltonian with parity-time-reversal ($\mathcal{PT}$) symmetry in a single trapped $^{40}$Ca$^+$ ion. We show that any two non-orthogonal states can become orthogonal subjected to time evolution of a $\mathcal{PT}$-symmetric Hamiltonian in both the $\mathcal{PT}$-symmetry preserving… ▽ More We experimentally demonstrate an unambiguous quantum state discrimination of two qubit states under a non-Hermitian Hamiltonian with parity-time-reversal ($\mathcal{PT}$) symmetry in a single trapped $^{40}$Ca$^+$ ion. We show that any two non-orthogonal states can become orthogonal subjected to time evolution of a $\mathcal{PT}$-symmetric Hamiltonian in both the $\mathcal{PT}$-symmetry preserving and broken regimes, thus can be discriminated deterministically. For a given pair of candidate states, we show that the parameters of the Hamiltonian must be confined in a proper range, within which there exists an optimal choice to realize quantum brachistochrone for the fastest orthogonalization. Besides, we provide a clear geometric picture and some analytic results to understand the main conclusions. Our work shows a promising application of non-Hermitian physics in quantum information processing. △ Less

Submitted 28 February, 2025; originally announced February 2025.

Comments: 6 pages, 4 figures

Detecting quantum steering in networks

Authors: Ming-Xiao Li, Yuqi Li, Ya Xi, Chang-Yue Zhang, Ying-Zheng Wang, Rui-Bin Xu, Shao-Ming Fei, Zhu-Jun Zheng

Abstract: Quantum networks promise an unprecedented leap in semi-device-independent communication and security by capitalizing on quantum steering. However, current methods for assessing quantum network steering are constrained to specific cases. In this work, we introduce the network-Clauser-Horn-Shimony-Holt-like inequality for investigating network steering independent of entanglement source characterist… ▽ More Quantum networks promise an unprecedented leap in semi-device-independent communication and security by capitalizing on quantum steering. However, current methods for assessing quantum network steering are constrained to specific cases. In this work, we introduce the network-Clauser-Horn-Shimony-Holt-like inequality for investigating network steering independent of entanglement source characteristics. We employ this inequality to detect full network steering in both single-node and multinode repeater networks and assess the tolerance of various noise models. Under a specific noise model, our method is used to compute the bound of semi-device-independent communication distance. Through case studies, we also demonstrate that our method, as a semi-device-independent entanglement witness, is more suitable for settings requiring Bell measurements compared to network Bell inequality. These findings open new avenues for broader ways to detect quantum steering independent of entanglement sources. △ Less

Submitted 29 January, 2025; originally announced January 2025.

Comments: 14 pages, 7 figures

Journal ref: Physical Review A 111, 012624 (2025)

Coarse-grained Bootstrap of Quantum Many-body Systems

Authors: Minjae Cho, Colin Oscar Nancarrow, Petar Tadić, Yuan Xin, Zechuan Zheng

Abstract: We present a new computational framework combining coarse-graining techniques with bootstrap methods to study quantum many-body systems. The method efficiently computes rigorous upper and lower bounds on both zero- and finite-temperature expectation values of any local observables of infinite quantum spin chains. This is achieved by using tensor networks to coarse-grain bootstrap constraints, incl… ▽ More We present a new computational framework combining coarse-graining techniques with bootstrap methods to study quantum many-body systems. The method efficiently computes rigorous upper and lower bounds on both zero- and finite-temperature expectation values of any local observables of infinite quantum spin chains. This is achieved by using tensor networks to coarse-grain bootstrap constraints, including positivity, translation invariance, equations of motion, and energy-entropy balance inequalities. Coarse-graining allows access to constraints from significantly larger subsystems than previously possible, yielding tighter bounds compared to those obtained without coarse-graining. △ Less

Submitted 22 November, 2025; v1 submitted 10 December, 2024; originally announced December 2024.

Comments: v1: 10 figures, public code included, v2: moved example code to anc folder, v3: minor error fixed and small adjustments, v4: small adjustments

Pattern Tree: Enhancing Efficiency in Quantum Circuit Optimization Based on Pattern-matching

Authors: Mingyu Chen, Yu Zhang, Zhaoyu Zheng, Yongshang Li, Haoning Deng

Abstract: Quantum circuit optimization is essential for improving the performance of quantum algorithms, particularly on Noisy Intermediate-Scale Quantum (NISQ) devices with limited qubit connectivity and high error rates. Pattern matching has proven to be an effective technique for identifying and optimizing subcircuits by replacing them with functionally equivalent, efficient versions, including reducing… ▽ More Quantum circuit optimization is essential for improving the performance of quantum algorithms, particularly on Noisy Intermediate-Scale Quantum (NISQ) devices with limited qubit connectivity and high error rates. Pattern matching has proven to be an effective technique for identifying and optimizing subcircuits by replacing them with functionally equivalent, efficient versions, including reducing circuit depth and facilitating platform portability. However, existing approaches face challenges in handling large-scale circuits and numerous transformation rules, often leading to redundant matches and increased compilation time. In this study, we propose a novel framework for quantum circuit optimization based on pattern matching to enhance its efficiency. Observing redundancy in applying existing transformation rules, our method employs a pattern tree structure to organize these rules, reducing redundant operations during the execution of the pattern-matching algorithm and improving matching efficiency. We design and implement a compilation framework to demonstrate the practicality of the pattern tree approach. Experimental results show that pattern-tree-based pattern matching can reduce execution time by an average of 20% on a well-accepted benchmark set. Furthermore, we analyze how to build a pattern tree to maximize the optimization of compilation time. The evaluation results demonstrate that our approach has the potential to optimize compilation time by 90%. △ Less

Submitted 9 December, 2024; originally announced December 2024.

Comments: 18 pages, 9 figures

Purity and construction of arbitrary dimensional $k$-uniform mixed states

Authors: Xiao Zhang, Shanqi Pang, Shao-Ming Fei, Zhu-Jun Zheng

Abstract: k-uniform mixed states are a significant class of states characterized by all k-party reduced states being maximally mixed. Novel methodologies are constructed for constructing k-uniform mixed states with the highest possible purity. By using the orthogonal partition of orthogonal arrays, a series of new $k$-uniform mixed states is derived. Consequently, an infinite number of higher-dimensional k-… ▽ More k-uniform mixed states are a significant class of states characterized by all k-party reduced states being maximally mixed. Novel methodologies are constructed for constructing k-uniform mixed states with the highest possible purity. By using the orthogonal partition of orthogonal arrays, a series of new $k$-uniform mixed states is derived. Consequently, an infinite number of higher-dimensional k-uniform mixed states, including those with highest purity, can be generated. △ Less

Submitted 28 August, 2024; originally announced August 2024.

Journal ref: Adv. Quantum Technol. 2024, 2400245

Communication with Quantum Catalysts

Authors: Yuqi Li, Junjing Xing, Dengke Qu, Lei Xiao, Zhaobing Fan, Zhu-Jun Zheng, Haitao Ma, Peng Xue, Kishor Bharti, Dax Enshan Koh, Yunlong Xiao

Abstract: Communication is essential for advancing science and technology. Quantum communication, in particular, benefits from the use of catalysts. During the communication process, these catalysts enhance performance while remaining unchanged. Although chemical catalysts that undergo deactivation typically perform worse than those that remain unaffected, quantum catalysts, referred to as embezzling cataly… ▽ More Communication is essential for advancing science and technology. Quantum communication, in particular, benefits from the use of catalysts. During the communication process, these catalysts enhance performance while remaining unchanged. Although chemical catalysts that undergo deactivation typically perform worse than those that remain unaffected, quantum catalysts, referred to as embezzling catalysts, can surprisingly outperform their non-deactivating counterparts despite experiencing slight alterations. In this work, we employ embezzling quantum catalysts to enhance the transmission of both quantum and classical information. Our results reveal that using embezzling catalysts augments the efficiency of information transmission across noisy quantum channels, ensuring a non-zero catalytic channel capacity. Furthermore, we introduce catalytic superdense coding, demonstrating how embezzling catalysts can enhance the transmission of classical information. Finally, we explore methods to reduce the dimensionality of catalysts, a step toward making quantum catalysis a practical reality. △ Less

Submitted 20 June, 2024; originally announced June 2024.

Comments: 16 pages, 9 figures. Comments welcome!

Journal ref: Quantum Science and Technology 10, 035044 (2025)

Quantum Krylov-Subspace Method Based Linear Solver

Authors: Rui-Bin Xu, Zhu-Jun Zheng, Zheng Zheng

Abstract: Despite the successful enhancement to the Harrow-Hassidim-Lloyd algorithm by Childs et al., who introduced the Fourier approach leveraging linear combinations of unitary operators, our research has identified non-trivial redundancies within this method. This finding points to a considerable potential for refinement. In this paper, we propose the quantum Krylov-subspace method (QKSM), which is a hy… ▽ More Despite the successful enhancement to the Harrow-Hassidim-Lloyd algorithm by Childs et al., who introduced the Fourier approach leveraging linear combinations of unitary operators, our research has identified non-trivial redundancies within this method. This finding points to a considerable potential for refinement. In this paper, we propose the quantum Krylov-subspace method (QKSM), which is a hybrid classical-quantum algorithm, to mitigate such redundancies. By integrating QKSM as a subroutine, we introduce the quantum Krylov-subspace method based linear solver that not only reduces computational redundancy but also enhances efficiency and accuracy. Extensive numerical experiments, conducted on systems with dimensions up to $2^{10} \times 2^{10}$, have demonstrated a significant reduction in computational resources and have led to more precise approximations. △ Less

Submitted 10 May, 2024; originally announced May 2024.

Genuinely nonlocal sets with smallest cardinality

Authors: Zong-Xing Xiong, Mao-Sheng Li, Bing Yu, Zhu-Jun Zheng, Lvzhou Li

Abstract: Recently, there is growing interest in the study of genuine nonlocality, which serves to explore the local accessability of global information encoded in orthogonal multipartite quantum states under scenarios where not all subsystems are joined together. For such form of nonlocality, a probably most fundamental question is upon what states it is prone to be manifested. To tackle this, we present i… ▽ More Recently, there is growing interest in the study of genuine nonlocality, which serves to explore the local accessability of global information encoded in orthogonal multipartite quantum states under scenarios where not all subsystems are joined together. For such form of nonlocality, a probably most fundamental question is upon what states it is prone to be manifested. To tackle this, we present in this work genuinely nonlocal sets with the smallest possible cardinality. We first show the existence of genuinely nonlocal sets of three pure states in arbitrary N-partite system. As a byproduct, this also gives new examples of strongly nonlocal sets with dramatically smaller cardinality than ever for all possible systems, settling some related questions effortlessly. Then, for mixed hypothetical states, we show that genuinely nonlocal sets of two even exist, regardless of the number of copies available. In particular, it turns out for both our constructions that certain genuinely entangled states necessarily exist, nontrivially indicating their potential of raising difficulty in locally accessing multipartite quantum information. △ Less

Submitted 12 April, 2026; v1 submitted 16 March, 2024; originally announced March 2024.

Filter-free high-performance single photon emission from a quantum dot in a Fabry-Perot microcavity

Authors: Zhixuan Rao, Jiawei Yang, Changkun Song, Mujie Rao, Ziyang Zheng, Luyu Liu, Xuebin Peng, Ying Yu, Siyuan Yu

Abstract: Combining resonant excitation with Purcell-enhanced single quantum dots (QDs) stands out as a prominent strategy for realizing high performance solid-state single photon sources. However, optimizing photon efficiency requires addressing challenges associated with effectively separating the excitation laser from QDs' emission. Traditionally, this involves polarization filtering, which limits the ac… ▽ More Combining resonant excitation with Purcell-enhanced single quantum dots (QDs) stands out as a prominent strategy for realizing high performance solid-state single photon sources. However, optimizing photon efficiency requires addressing challenges associated with effectively separating the excitation laser from QDs' emission. Traditionally, this involves polarization filtering, which limits the achievable polarization directions and the scalability of photonic states. In this study, we have successfully tackled this challenge by employing spatially-orthogonal resonant excitation of QDs, deterministically coupled to monolithic Fabry-Perot microcavities. Leveraging the membrane cavity structures, we have achieved filter-free single photon resonant fluorescence. The resulting source produces single photons with a simultaneous high extraction efficiency of 0.87, purity of 0.9045(4), and indistinguishability of 0.963(4). △ Less

Submitted 17 March, 2024; v1 submitted 18 February, 2024; originally announced February 2024.

Comments: 9 pages, 4 figures

Learnability of a hybrid quantum-classical neural network for graph-structured quantum data

Authors: Yanying Liang, Sile Tang, Zhehao Yi, Haozhen Situ, Zhu-Jun Zheng

Abstract: Graph-structured data commonly arise in many real-world applications, and this extends naturally into the quantum setting, where quantum data with inherent graph structures are frequently generated by typical quantum data sources. However, existing state-of-the-art models often lack training and evaluation on deeper quantum neural networks. In this work, we design a hybrid quantum-classical neural… ▽ More Graph-structured data commonly arise in many real-world applications, and this extends naturally into the quantum setting, where quantum data with inherent graph structures are frequently generated by typical quantum data sources. However, existing state-of-the-art models often lack training and evaluation on deeper quantum neural networks. In this work, we design a hybrid quantum-classical neural network with deep residual learning, termed Res-HQCNN, specifically designed to handle graph-structured quantum data.Building upon this architecture, we systematically explore the interplay between residual block structures and graph information in both training and testing phases. Through extensive experiments, we demonstrate that incorporating graph structure information into the quantum data significantly improves learning efficiency compared to the existing model. Additionally, we conduct comparative experiments to evaluate the effectiveness of residual blocks. Our results show that the residual structure enables deeper Res-HQCNN models to learn graph-structured quantum data more efficiently and accurately. △ Less

Submitted 25 August, 2025; v1 submitted 28 January, 2024; originally announced January 2024.

Comments: 25 pages,10 figures

Polygamy relations for tripartite and multipartite quantum systems

Authors: Yanying Liang, Haozhen Situ, Zhu-Jun Zheng

Abstract: We study the polygamy property for tripartite and multipartite quantum systems. In tripartite system, we build a solution set for polygamy in tripartite system and find a lower bound of the set, which can be a sufficient and necessary condition for any quantum entanglement of assistance $Q$ to be polygamous. In multipartite system, we firstly provide generalized definitions for polygamy in two kin… ▽ More We study the polygamy property for tripartite and multipartite quantum systems. In tripartite system, we build a solution set for polygamy in tripartite system and find a lower bound of the set, which can be a sufficient and necessary condition for any quantum entanglement of assistance $Q$ to be polygamous. In multipartite system, we firstly provide generalized definitions for polygamy in two kind of divisions of $n$-qubit systems, and then build polygamy inequalities with a polygamy power $β$, repectively. Moreover, we use right triangle and tetrahedron to explain our polygamy relations according to the new definitions. △ Less

Submitted 9 January, 2024; v1 submitted 25 December, 2023; originally announced December 2023.

Comments: 8 pages, 2 figures

Witnessing quantum coherence with prior knowledge of observables

Authors: Mao-Sheng Li, Wen Xu, Shao-Ming Fei, Zhu-Jun Zheng, Yan-Ling Wang

Abstract: Quantum coherence is the key resource in quantum technologies including faster computing, secure communication and advanced sensing. Its quantification and detection are, therefore, paramount within the context of quantum information processing. Having certain priori knowledge on the observables may enhance the efficiency of coherence detection. In this work, we posit that the trace of the observa… ▽ More Quantum coherence is the key resource in quantum technologies including faster computing, secure communication and advanced sensing. Its quantification and detection are, therefore, paramount within the context of quantum information processing. Having certain priori knowledge on the observables may enhance the efficiency of coherence detection. In this work, we posit that the trace of the observables is a known quantity. Our investigation confirms that this assumption indeed extends the scope of coherence detection capabilities. Utilizing this prior knowledge of the trace of the observables, we establish a series of coherence detection criteria. We investigate the detection capabilities of these coherence criteria from diverse perspectives and ultimately ascertain the existence of four distinct and inequivalent criteria. These findings contribute to the deepening of our understanding of coherence detection methodologies, thereby potentially opening new avenues for advancements in quantum technologies. △ Less

Submitted 17 November, 2023; originally announced November 2023.

Comments: 9 pages, 3 figures

Journal ref: Physical Review A 109 032422 (2024)

Tunable quantum dots in monolithic Fabry-Perot microcavities for high-performance single-photon sources

Authors: Jiawei Yang, Yan Chen, Zixuan Rao, Ziyang Zheng, Changkun Song, Yujie Chen, Kaili Xiong, Pingxing Chen, Chaofan Zhang, Wei Wu, Ying Yu, Siyuan Yu

Abstract: Cavity-enhanced single quantum dots (QDs) are the main approach towards ultra-high-performance solid-state quantum light sources for scalable photonic quantum technologies. Nevertheless, harnessing the Purcell effect requires precise spectral and spatial alignment of the QDs' emission with the cavity mode, which is challenging for most cavities. Here we have successfully integrated miniaturized Fa… ▽ More Cavity-enhanced single quantum dots (QDs) are the main approach towards ultra-high-performance solid-state quantum light sources for scalable photonic quantum technologies. Nevertheless, harnessing the Purcell effect requires precise spectral and spatial alignment of the QDs' emission with the cavity mode, which is challenging for most cavities. Here we have successfully integrated miniaturized Fabry-Perot microcavities with a piezoelectric actuator, and demonstrated a bright single photon source derived from a deterministically coupled QD within this microcavity. Leveraging the cavity-membrane structures, we have achieved large spectral-tunability via strain tuning. On resonance, we have obtained a high Purcell factor of approximately 9. The source delivers single photons with simultaneous high extraction efficiency of 0.58, high purity of 0.956(2) and high indistinguishability of 0.922(4). Together with a small footprint, our scheme facilitates the scalable integration of indistinguishable quantum light sources on-chip, and therefore removes a major barrier to the solid-state quantum information platforms based on QDs. △ Less

Submitted 24 September, 2023; originally announced September 2023.

Comments: 12 pages, 4 figures

Beyond the mixture of generalized Pauli dephasing channels

Authors: Mao-Sheng Li, Wen Xu, Yan-Ling Wang, Zhu-Jun Zheng

Abstract: In recent times, there has been a growing scholarly focus on investigating the intricacies of quantum channel mixing. It has been commonly believed, based on intuition in the literature, that every generalized Pauli channel with dimensionality $d$ could be represented as a convex combination of $(d+1)$ generalized Pauli dephasing channels (see [Phys. Rev. A 103, 022605 (2021)] as a reference). To… ▽ More In recent times, there has been a growing scholarly focus on investigating the intricacies of quantum channel mixing. It has been commonly believed, based on intuition in the literature, that every generalized Pauli channel with dimensionality $d$ could be represented as a convex combination of $(d+1)$ generalized Pauli dephasing channels (see [Phys. Rev. A 103, 022605 (2021)] as a reference). To our surprise, our findings indicate the inaccuracy of this intuitive perspective. This has stimulated our interest in exploring the properties of convex combinations of generalized Pauli channels, beyond the restriction to just $(d+1)$ generalized Pauli dephasing channels. We demonstrate that many previously established properties still hold within this broader context. For instance, any mixture of invertible generalized Pauli channels retains its invertibility. It's worth noting that this property doesn't hold when considering the Weyl channels setting. Additionally, we demonstrate that every Pauli channel (for the case of $d=2$) can be represented as a mixture of $(d+1)$ Pauli dephasing channels, but this generalization doesn't apply to higher dimensions. This highlights a fundamental distinction between qubit and general qudit cases. In contrast to prior understanding, we show that non-invertibility of mixed channels is not a prerequisite for the resulting mapping to constitute a Markovian semigroup. △ Less

Submitted 9 September, 2023; originally announced September 2023.

Comments: 9 pages, 2 figures

Error Mitigated Metasurface-Based Randomized Measurement Schemes

Authors: Hang Ren, Yipei Zhang, Ze Zheng, Cuifeng Ying, Lei Xu, Mohsen Rahmani, K. Birgitta Whaley

Abstract: Estimating properties of quantum states via randomized measurements has become a significant part of quantum information science. In this paper, we design an innovative approach leveraging metasurfaces to perform randomized measurements on photonic qubits, together with error mitigation techniques that suppress realistic metasurface measurement noise. Through fidelity and purity estimation, we con… ▽ More Estimating properties of quantum states via randomized measurements has become a significant part of quantum information science. In this paper, we design an innovative approach leveraging metasurfaces to perform randomized measurements on photonic qubits, together with error mitigation techniques that suppress realistic metasurface measurement noise. Through fidelity and purity estimation, we confirm the capability of metasurfaces to implement randomized measurements and the unbiased nature of our error-mitigated estimator. Our findings show the potential of metasurface-based randomized measurement schemes in achieving robust and resource-efficient estimation of quantum state properties. △ Less

Submitted 19 April, 2024; v1 submitted 16 August, 2023; originally announced August 2023.

Multipartite concurrence of W-class states based on sub-partite quantum systems

Authors: Wei Chen, Yanmin Yang, Shao-Ming Fei, Zhu-Jun Zheng, Yan-Ling Wang

Abstract: We study the concurrence for arbitrary N-partite W-class states based on the (N-1)-partite partitions of subsystems by taking account to the structures of W-class states. By using the method of permutation and combination we give analytical formula of concurrence and some elegant relations between the multipartite concurrence and the (N-1)-partite concurrence for arbitrary multipartite W-class sta… ▽ More We study the concurrence for arbitrary N-partite W-class states based on the (N-1)-partite partitions of subsystems by taking account to the structures of W-class states. By using the method of permutation and combination we give analytical formula of concurrence and some elegant relations between the multipartite concurrence and the (N-1)-partite concurrence for arbitrary multipartite W-class states. Applying these relations we present better lower bounds of concurrence for multipartite mixed states. An example is given to demonstrate that our lower bounds can detect more entanglements. △ Less

Submitted 15 December, 2022; originally announced December 2022.

Exact solution of the boundary-dissipated transverse field Ising model: Structure of Liouvillian spectrum and dynamical duality

Authors: Zhen-Yu Zheng, Xueliang Wang, Shu Chen

Abstract: We study the boundary-dissipated transverse field Ising model described by a Lindblad Master equation and exactly solve its Liouvillian spectrum in the whole parameter space. By mapping the Liouvillian into a Su-Schrieffer-Heeger model with imaginary boundary potentials under a parity constraint, we solve the rapidity spectrum analytically and thus construct the Liouvillian spectrum strictly with… ▽ More We study the boundary-dissipated transverse field Ising model described by a Lindblad Master equation and exactly solve its Liouvillian spectrum in the whole parameter space. By mapping the Liouvillian into a Su-Schrieffer-Heeger model with imaginary boundary potentials under a parity constraint, we solve the rapidity spectrum analytically and thus construct the Liouvillian spectrum strictly with a parity constraint condition. Our results demonstrate that the Liouvillian spectrum displays four different structures, which are characterized by different numbers of segments. By analyzing the properties of rapidity spectrum, we can determine the phase boundaries between different spectrum structures analytically and prove the Liouvillian gap fulfilling a duality relation in the weak and strong dissipation region. Furthermore, we unveil the existence of a dynamical duality, i.e., the long-time relaxation dynamics exhibits almost the same dynamical behavior in the weak and strong dissipation region as long as the duality relation holds true. △ Less

Submitted 16 July, 2023; v1 submitted 9 December, 2022; originally announced December 2022.

Comments: 15 pages, 10 figures

Journal ref: Phys. Rev. B 108, 024404 (2023)

Distinguishability-based genuine nonlocality with genuine multipartite entanglement

Authors: Zong-Xing Xiong, Mao-Sheng Li, Zhu-Jun Zheng, Lvzhou Li

Abstract: A set of orthogonal multipartite quantum states is said to be distinguishability-based genuinely nonlocal (also genuinely nonlocal, for abbreviation) if the states are locally indistinguishable across any bipartition of the subsystems. This form of multipartite nonlocality, although more naturally arising than the recently popular "strong nonlocality" in the context of local distinguishability, re… ▽ More A set of orthogonal multipartite quantum states is said to be distinguishability-based genuinely nonlocal (also genuinely nonlocal, for abbreviation) if the states are locally indistinguishable across any bipartition of the subsystems. This form of multipartite nonlocality, although more naturally arising than the recently popular "strong nonlocality" in the context of local distinguishability, receives much less attention. In this work, we study the distinguishability-based genuine nonlocality of a typical type of genuine multipartite entangled states -- the d-dimensional GHZ states, featuring systems with local dimension not limited to 2. In the three-partite case, we find the existence of small genuinely nonlocal sets consisting of these states: we show that the cardinality can at least scale down to linear in the local dimension d, with the linear factor l = 1. Specifically, the method we use is semidefinite program and the GHZ states to construct these sets are special ones which we call "GHZ-lattices". This result might arguably suggest a significant gap between the strength of strong nonlocality and the distinguishability-based genuine nonlocality. Moreover, we put forward the notion of (s,n)-threshold distinguishability and utilizing a similar method, we successfully construct (2,3)-threshold sets consisting of GHZ states in three-partite systems. △ Less

Submitted 21 November, 2023; v1 submitted 4 November, 2022; originally announced November 2022.

Sharing tripartite nonlocality sequentially by arbitrarily many independent observers

Authors: Ya Xi Mao-Sheng Li Libin Fu, Zhu-Jun Zheng

Abstract: There exist bipartite entangled states whose violations of Clauser-Horne-Shimony-Holt (CHSH) Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs [Phys. Rev. Lett. 125, 090401 (2020)]. Here we consider its analogues for tripartite systems: a tripartite entangled state is shared among Alice, Bob and multiple Charlies. The first Charlie measures his qubit and then p… ▽ More There exist bipartite entangled states whose violations of Clauser-Horne-Shimony-Holt (CHSH) Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs [Phys. Rev. Lett. 125, 090401 (2020)]. Here we consider its analogues for tripartite systems: a tripartite entangled state is shared among Alice, Bob and multiple Charlies. The first Charlie measures his qubit and then passes his qubit to the next Charlie who measures again with other measurements and so on. The goal is to maximize the number of Charlies that can observe some kind of nonlocality with the single Alice and Bob. It has been shown that at most two Charlies could share genuine nonlocality of the Greenberger-Horne-Zeilinger (GHZ) state via the violation of Svetlichny inequality with Alice and Bob [Quantum Inf. Process. 18, 42 (2019) and Phys. Rev. A 103, 032216 (2021)]. In this work, we show that arbitrarily many Charlies can have standard nonlocality (via violations of Mermin inequality) and some other kind of genuine nonlocality (which is known as genuinely nonsignal nonlocality) with the single Alice and single Bob. △ Less

Submitted 6 November, 2023; v1 submitted 1 July, 2022; originally announced July 2022.

Comments: 12 pages, 2figure

Journal ref: Physical Review A 107, 062419 (2023)

Dynamic quantum-enhanced sensing without entanglement in central spin systems

Authors: Wenkui Ding, Yanxia Liu, Zhenyu Zheng, Shu Chen

Abstract: We propose a dynamic quantum sensing scheme by using a quantum many-spin system composed of a central spin interacting with many surrounding spins. Starting from a generalized Ising ring model, we investigate the error propagation formula of the central spin and it indicates that Heisenberg scaling can be reached while the probe state only needs to be a product state. Particularly, we derive an an… ▽ More We propose a dynamic quantum sensing scheme by using a quantum many-spin system composed of a central spin interacting with many surrounding spins. Starting from a generalized Ising ring model, we investigate the error propagation formula of the central spin and it indicates that Heisenberg scaling can be reached while the probe state only needs to be a product state. Particularly, we derive an analytical form of the dynamic quantum Fisher information in a limit case, which explicitly exhibits the Heisenberg scaling. By comparing with numerical results, we demonstrate that the general case can be well approximated by the analytical result when the coupling strength among the surrounding spins is much weaker than the coupling strength between the central and surrounding spins. This analytic result guides us to find the appropriate probe state and the proper measurement time, to achieve the Heisenberg scaling in realistic situations. Furthermore, we investigate various effects which are important in practical quantum systems, including the central spin Zeeman term, the anisotropy of the hyperfine interaction and the inhomogeneity of the hyperfine coupling strength. Our result indicates that the dynamic quantum-enhanced sensing scheme seems feasible in realistic quantum central spin systems, like semiconductor quantum dots. △ Less

Submitted 30 April, 2022; originally announced May 2022.

Genuine hidden nonlocality without entanglement: from the perspective of local discrimination

Authors: Mao-Sheng Li, Zhu-Jun Zheng

Abstract: Quantum nonlocality without entanglement is a fantastic phenomenon in quantum theory. This kind of quantum nonlocality is based on the task of local discrimination of quantum states. Recently, Bandyopadhyay and Halder [Phys. Rev. A 104, L050201 (2021)] studied the problem: is there any set of orthogonal states which can be locally distinguishable, but under some orthogonality preserving local meas… ▽ More Quantum nonlocality without entanglement is a fantastic phenomenon in quantum theory. This kind of quantum nonlocality is based on the task of local discrimination of quantum states. Recently, Bandyopadhyay and Halder [Phys. Rev. A 104, L050201 (2021)] studied the problem: is there any set of orthogonal states which can be locally distinguishable, but under some orthogonality preserving local measurement, each outcome will lead to a locally indistinguishable set. We say that the set with such property has hidden nonlocality. Moreover, if such phenomenon can not arise from discarding subsystems which is termed as local irredundancy, we call it genuine hidden nonlocality. There, they presented several sets of entangled states with genuine hidden nonlocality. However, they doubted the existence of a set without entanglement but with genuine hidden nonlocality. In this paper, we eliminate this doubt by constructing a series of sets without entanglement but whose nonlocality can be genuinely activated. We derive a method to tackle with the local irredundancy problem which is a key tricky for the systems whose local dimensions are composite numbers. As Bandyopadhyay and Halder have been pointed out, sets with genuine hidden nonloclity would lead to some applications on the data hiding. △ Less

Submitted 5 January, 2022; v1 submitted 4 November, 2021; originally announced November 2021.

Comments: 13 pages, 6 figures, add one more example

Quantum key distribution over noisy channels by the testing state method

Authors: Hao Shu, Chang-Yue Zhang, Yue-Qiu Chen, Zhu-Jun Zheng, Shao-Ming Fei

Abstract: Quantum key distribution(QKD) might be the most famous application of quantum information theory. The idea of QKD is not difficult to understand but in practical implementations, many problems are needed to be solved, for example, the noise of the channels. Previous works usually discuss the estimate of the channels and employ error-correcting procedures, whose feasibility and efficiency depend on… ▽ More Quantum key distribution(QKD) might be the most famous application of quantum information theory. The idea of QKD is not difficult to understand but in practical implementations, many problems are needed to be solved, for example, the noise of the channels. Previous works usually discuss the estimate of the channels and employ error-correcting procedures, whose feasibility and efficiency depend on the strength of the noise, or assist with entanglement distillation procedures, which often result in a large consumption of states while not all states can be distilled. This paper aims to study QKD over noisy channels including Pauli noises, amplitude damping noises, phase damping noises, collective noises as well as mixtures of them, in any strength without distillations. We provide a method, called the testing state method, to implement QKD protocols without errors over arbitrarily strength noisy channels. The method can be viewed as an error-correcting procedure, and can also be employed for other tasks. △ Less

Submitted 29 July, 2023; v1 submitted 5 July, 2021; originally announced July 2021.

Comments: 11 pages

Journal ref: International Journal of Theoretical Physics (2023)

Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays

Authors: Shanqi Pang, Xiao Zhang, Shao-Ming Fei, Zhu-Jun Zheng

Abstract: Quantum multipartite entangled states play significant roles in quantum information processing. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant mixed orthogonal arrays (IrMOAs) and thus provide positive answers to two open problems. The first is the extension of the method for constructing homogeneous systems from orthogonal arrays (O… ▽ More Quantum multipartite entangled states play significant roles in quantum information processing. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant mixed orthogonal arrays (IrMOAs) and thus provide positive answers to two open problems. The first is the extension of the method for constructing homogeneous systems from orthogonal arrays (OAs) to heterogeneous multipartite systems with different individual levels. The second is the existence of $k$-uniform states in heterogeneous quantum systems. We present explicit constructions of two and three-uniform states for arbitrary heterogeneous multipartite systems with coprime individual levels, and characterize the entangled states in heterogeneous systems consisting of subsystems with nonprime power dimensions as well. Moreover, we obtain infinite classes of $k$-uniform states for heterogeneous multipartite systems for any $k\geq2$. The non-existence of a class of IrMOAs is also proved. △ Less

Submitted 29 April, 2021; originally announced April 2021.

Journal ref: Quant. Inform. Processing 20 (2021) 156

Monogamy relations and upper bounds for the generalized $W$-class states using Rényi-$α$ entropy

Authors: Yanying Liang, Zhu-Jun Zheng, Chuan-Jie Zhu

Abstract: We investigate monogamy relations and upper bounds for generalized $W$-class states related to the Rényi-$α$ entropy. First, we present an analytical formula on Rényi-$α$ entanglement (R$α$E) and Rényi-$α$ entanglement of assistance (REoA) of a reduced density matrix for a generalized $W$-class states. According to the analytical formula, we show monogamy and polygamy relations for generalized… ▽ More We investigate monogamy relations and upper bounds for generalized $W$-class states related to the Rényi-$α$ entropy. First, we present an analytical formula on Rényi-$α$ entanglement (R$α$E) and Rényi-$α$ entanglement of assistance (REoA) of a reduced density matrix for a generalized $W$-class states. According to the analytical formula, we show monogamy and polygamy relations for generalized $W$-class states in terms of R$α$E and REoA. Then we give the upper bounds for generalized $W$-class states in terms of R$α$E. Next, we provide tighter monogamy relations for generalized $W$-class states in terms of concurrence and convex-roof extended negativity and obtain the monogamy relations for R$α$E by the analytical expression between R$α$E and concurrence. Finally, we apply our results into quantum games and present a new bound of the nonclassicality of quantum games restricting to generalized $W$-class states. △ Less

Submitted 30 April, 2020; originally announced October 2020.

Comments: 17 pages, 3 figures