Coherent information for CSS codes under decoherence
Authors:
Ryotaro Niwa,
Jong Yeon Lee
Abstract:
Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and fractons. Recent studies have revealed that the decoding transition for these QECCs could be intrinsically captured by calculating information-theoretic quantiti…
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Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and fractons. Recent studies have revealed that the decoding transition for these QECCs could be intrinsically captured by calculating information-theoretic quantities from the mixed state. Here we perform a simple analytic calculation of the coherent information for general CSS codes under local incoherent Pauli errors via diagonalization of the density matrices and mapping to classical statistical mechanical (SM) models. Our result establishes a rigorous connection between the decoding transition of the quantum code and the phase transition in the random classical SM model. It is also directly confirmed for CSS codes that exact error correction is possible if and only if the maximum-likelihood (ML) decoder always succeeds in the thermodynamic limit. Thus, the fundamental threshold is saturated by the optimal decoder.
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Submitted 6 July, 2025; v1 submitted 2 July, 2024;
originally announced July 2024.
Magnetic origin of high-energy kink structure in heavily electron-doped Li$_{1+x}$FeAs
Authors:
T. Hajiri,
T. Ito,
R. Niwa,
S. Hirate,
M. Matsunami,
B. H. Min,
Y. S. Kwon,
S. Kimura
Abstract:
We report the origin of a high-energy kink structure of heavily electron-doped nonsuperconducting Li$_{1+x}$FeAs observed by three-dimensional angle-resolved photoemission spectroscopy. The $d_{xy}$ orbital at the center of the Brillouin zone is strongly renormalized, indicating stronger electron correlation, exceeding that of stoichiometric LiFeAs despite the fact that the orbital characters of a…
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We report the origin of a high-energy kink structure of heavily electron-doped nonsuperconducting Li$_{1+x}$FeAs observed by three-dimensional angle-resolved photoemission spectroscopy. The $d_{xy}$ orbital at the center of the Brillouin zone is strongly renormalized, indicating stronger electron correlation, exceeding that of stoichiometric LiFeAs despite the fact that the orbital characters of all bands remain unchanged. Two types of kink structure on the $d_{yz}$ band were identified: an isotropic kink at the binding energy of 20 meV, and another kink located at 100 meV observed only in the (110) direction. The higher-energy kink is considered to originate from a magnetic interaction, because the peak energy is consistent with that of a spin excitation.
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Submitted 30 January, 2013; v1 submitted 28 December, 2012;
originally announced December 2012.