A change of perspective: switching quantum reference frames via a perspective-neutral framework

Augustin Vanrietvelde¹, Philipp A. Hoehn^1,2, Flaminia Giacomini^1,2, and Esteban Castro-Ruiz^1,2

¹Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
²Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria

Published:	2020-01-27, volume 4, page 225
Eprint:	arXiv:1809.00556v4
Doi:	https://doi.org/10.22331/q-2020-01-27-225
Citation:	Quantum 4, 225 (2020).

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Abstract

Treating reference frames fundamentally as quantum systems is inevitable in quantum gravity and also in quantum foundations once considering laboratories as physical systems. Both fields thereby face the question of how to describe physics relative to quantum reference systems and how the descriptions relative to different such choices are related. Here, we exploit a fruitful interplay of ideas from both fields to begin developing a unifying approach to transformations among quantum reference systems that ultimately aims at encompassing both quantum and gravitational physics. In particular, using a gravity inspired symmetry principle, which enforces physical observables to be relational and leads to an inherent redundancy in the description, we develop a perspective-neutral structure, which contains all frame perspectives at once and via which they are changed. We show that taking the perspective of a specific frame amounts to a fixing of the symmetry related redundancies in both the classical and quantum theory and that changing perspective corresponds to a symmetry transformation. We implement this using the language of constrained systems, which naturally encodes symmetries. Within a simple one-dimensional model, we recover some of the quantum frame transformations of [1], embedding them in a perspective-neutral framework. Using them, we illustrate how entanglement and classicality of an observed system depend on the quantum frame perspective. Our operational language also inspires a new interpretation of Dirac and reduced quantized theories within our model as perspective-neutral and perspectival quantum theories, respectively, and reveals the explicit link between them. In this light, we suggest a new take on the relation between a `quantum general covariance' and the diffeomorphism symmetry in quantum gravity.

► BibTeX data

@article{Vanrietvelde2020changeof,
  doi = {10.22331/q-2020-01-27-225},
  url = {https://doi.org/10.22331/q-2020-01-27-225},
  title = {A change of perspective: switching quantum reference frames via a perspective-neutral framework},
  author = {Vanrietvelde, Augustin and Hoehn, Philipp A. and Giacomini, Flaminia and Castro-Ruiz, Esteban},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {225},
  month = jan,
  year = {2020}
}

► References

[1] F. Giacomini, E. Castro-Ruiz, and Č. Brukner, ``Quantum mechanics and the covariance of physical laws in quantum reference frames,'' Nature communications 10 no. 1, (2019) 494, arXiv:1712.07207 [quant-ph].
https://doi.org/10.1038/s41467-018-08155-0
arXiv:1712.07207

[2] A. Vanrietvelde, P. A. Höhn, and F. Giacomini, ``Switching quantum reference frames in the N-body problem and the absence of global relational perspectives,'' arXiv:1809.05093 [quant-ph].
arXiv:1809.05093

[3] P. A. Höhn and A. Vanrietvelde, ``How to switch between relational quantum clocks,'' arXiv:1810.04153 [gr-qc].
arXiv:1810.04153

[4] P. A. Höhn, ``Switching Internal Times and a New Perspective on the Wave Function of the Universe,'' Universe 5 no. 5, (2019) 116, arXiv:1811.00611 [gr-qc].
https://doi.org/10.3390/universe5050116
arXiv:1811.00611

[5] P. A. Höhn, ``Effective changes of quantum reference systems in quantum phase space,'' to appear (2020).

[6] Y. Aharonov and L. Susskind, ``Charge Superselection Rule,'' Phys. Rev. 155 (1967) 1428–1431.
https://doi.org/10.1103/PhysRev.155.1428

[7] B. S. DeWitt, ``Quantum theory of gravity. I. The canonical theory,'' Phys.Rev. 160 (1967) 1113–1148.
https://doi.org/10.1103/PhysRev.160.1113

[8] C. Rovelli, Quantum Gravity. Cambridge University Press, 2004.
https://doi.org/10.1017/CBO9780511755804

[9] J. Barbour and B. Bertotti, ``Mach's principle and the structure of dynamical theories,'' Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 382 no. 1783, (1982) 295–306.
https://doi.org/10.1098/rspa.1982.0102

[10] F. Mercati, Shape Dynamics: Relativity and Relationalism. Oxford University Press, 2018.
https://doi.org/10.1093/oso/9780198789475.001.0001

[11] C. Rovelli, ``Quantum reference systems,'' Class.Quant.Grav. 8 (1991) 317–332.
https://doi.org/10.1088/0264-9381/8/2/012

[12] C. Rovelli, ``What is observable in classical and quantum gravity?,'' Class.Quant.Grav. 8 (1991) 297–316.
https://doi.org/10.1088/0264-9381/8/2/011

[13] K. Kuchař, ``Time and interpretations of quantum gravity,'' Int.J.Mod.Phys.Proc.Suppl. D20 (2011) 3–86. Originally published in the Proc. 4th Canadian Conf. on General Relativity and Relativistic Astrophysics, eds. G. Kunstatter, D. Vincent and J. Williams (World Scientific, Singapore, 1992).
https://doi.org/10.1142/S0218271811019347

[14] C. Isham, ``Canonical quantum gravity and the problem of time,'' in Integrable Systems, Quantum Groups, and Quantum Field Theories, pp. 157–287, Kluwer Academic Publishers, 1993, arXiv:gr-qc/9210011 [gr-qc].
https://doi.org/10.1007/978-94-011-1980-1_6
arXiv:gr-qc/9210011

[15] J. D. Brown and K. V. Kuchař, ``Dust as a standard of space and time in canonical quantum gravity,'' Phys.Rev. D51 (1995) 5600–5629, arXiv:gr-qc/9409001 [gr-qc].
https://doi.org/10.1103/PhysRevD.51.5600
arXiv:gr-qc/9409001

[16] B. Dittrich, ``Partial and complete observables for Hamiltonian constrained systems,'' Gen.Rel.Grav. 39 (2007) 1891–1927, arXiv:gr-qc/0411013 [gr-qc].
https://doi.org/10.1007/s10714-007-0495-2
arXiv:gr-qc/0411013

[17] B. Dittrich, ``Partial and complete observables for canonical General Relativity,'' Class.Quant.Grav. 23 (2006) 6155–6184, arXiv:gr-qc/0507106 [gr-qc].
https://doi.org/10.1088/0264-9381/23/22/006
arXiv:gr-qc/0507106

[18] J. Tambornino, ``Relational observables in gravity: A review,'' SIGMA 8 (2012) 017, arXiv:1109.0740 [gr-qc].
https://doi.org/10.3842/SIGMA.2012.017
arXiv:1109.0740

[19] T. Thiemann, Modern Canonical Quantum General Relativity. Cambridge University Press, 2007.
https://doi.org/10.1017/CBO9780511755682

[20] B. Dittrich, P. A. Höhn, T. A. Koslowski, and M. I. Nelson, ``Can chaos be observed in quantum gravity?,'' Phys. Lett. B769 (2017) 554–560, arXiv:1602.03237 [gr-qc].
https://doi.org/10.1016/j.physletb.2017.02.038
arXiv:1602.03237

[21] B. Dittrich, P. A. Höhn, T. A. Koslowski, and M. I. Nelson, ``Chaos, Dirac observables and constraint quantization,'' arXiv:1508.01947 [gr-qc].
arXiv:1508.01947

[22] M. Bojowald, P. A. Höhn, and A. Tsobanjan, ``An Effective approach to the problem of time,'' Class. Quant. Grav. 28 (2011) 035006, arXiv:1009.5953 [gr-qc].
https://doi.org/10.1088/0264-9381/28/3/035006
arXiv:1009.5953

[23] M. Bojowald, P. A. Höhn, and A. Tsobanjan, ``Effective approach to the problem of time: general features and examples,'' Phys.Rev. D83 (2011) 125023, arXiv:1011.3040 [gr-qc].
https://doi.org/10.1103/PhysRevD.83.125023
arXiv:1011.3040

[24] P. A. Höhn, E. Kubalova, and A. Tsobanjan, ``Effective relational dynamics of a nonintegrable cosmological model,'' Phys.Rev. D86 (2012) 065014, arXiv:1111.5193 [gr-qc].
https://doi.org/10.1103/PhysRevD.86.065014
arXiv:1111.5193

[25] Y. Aharonov and L. Susskind, ``Observability of the sign change of spinors under $2{\pi}$ rotations,'' Phys. Rev. 158 (Jun, 1967) 1237–1238.
https://doi.org/10.1103/PhysRev.158.1237

[26] Y. Aharonov and T. Kaufherr, ``Quantum frames of reference,'' Phys. Rev. D 30 (Jul, 1984) 368–385.
https://doi.org/10.1103/PhysRevD.30.368

[27] S. D. Bartlett, T. Rudolph, and R. W. Spekkens, ``Reference frames, superselection rules, and quantum information,'' Rev. Mod. Phys. 79 (2007) 555–609, arXiv:quant-ph/0610030.
https://doi.org/10.1103/RevModPhys.79.555
arXiv:quant-ph/0610030

[28] S. D. Bartlett, T. Rudolph, R. W. Spekkens, and P. S. Turner, ``Quantum communication using a bounded-size quantum reference frame,'' New Journal of Physics 11 no. 6, (2009) 063013, arXiv:0812.5040 [quant-ph].
https://doi.org/10.1088/1367-2630/11/6/063013
arXiv:0812.5040

[29] G. Gour and R. W. Spekkens, ``The resource theory of quantum reference frames: manipulations and monotones,'' New Journal of Physics 10 no. 3, (2008) 033023, arXiv:0711.0043 [quant-ph].
arXiv:0711.0043

[30] M. C. Palmer, F. Girelli, and S. D. Bartlett, ``Changing quantum reference frames,'' Phys. Rev. A89 no. 5, (2014) 052121, arXiv:1307.6597 [quant-ph].
https://doi.org/10.1103/PhysRevA.89.052121
arXiv:1307.6597

[31] S. D. Bartlett, T. Rudolph, R. W. Spekkens, and P. S. Turner, ``Degradation of a quantum reference frame,'' New Journal of Physics 8 no. 4, (2006) 58, arXiv:1307.6597 [quant-ph].
arXiv:quant-ph/0602069

[32] A. R. Smith, M. Piani, and R. B. Mann, ``Quantum reference frames associated with noncompact groups: The case of translations and boosts and the role of mass,'' Physical Review A 94 no. 1, (2016) 012333, arXiv:1602.07696 [quant-ph].
https://doi.org/10.1103/PhysRevA.94.012333
arXiv:1602.07696

[33] D. Poulin and J. Yard, ``Dynamics of a quantum reference frame,'' New Journal of Physics 9 no. 5, (2007) 156, arXiv:quant-ph/0612126.
arXiv:quant-ph/0612126

[34] M. Skotiniotis, B. Toloui, I. T. Durham, and B. C. Sanders, ``Quantum frameness for $cpt$ symmetry,'' Phys. Rev. Lett. 111 (Jul, 2013) 020504, arXiv:1306.6114 [quant-ph].
https://doi.org/10.1103/PhysRevLett.111.020504
arXiv:1306.6114

[35] L. Loveridge, P. Busch, and T. Miyadera, ``Relativity of quantum states and observables,'' EPL (Europhysics Letters) 117 no. 4, (2017) 40004, arXiv:arXiv:1604.02836 [quant-ph].
https://doi.org/10.1209/0295-5075/117/40004
arXiv:1604.02836

[36] J. Pienaar, ``A relational approach to quantum reference frames for spins,'' arXiv:1601.07320 [quant-ph] (2016).
arXiv:1601.07320

[37] R. M. Angelo, N. Brunner, S. Popescu, A. J. Short, and P. Skrzypczyk, ``Physics within a quantum reference frame,'' Journal of Physics A: Mathematical and Theoretical 44 no. 14, (2011) 145304, arXiv:1007.2292 [quant-ph].
https://doi.org/10.1088/1751-8113/44/14/145304
arXiv:1007.2292

[38] P. A. Höhn and M. P. Müller, ``An operational approach to spacetime symmetries: Lorentz transformations from quantum communication,'' New J. Phys. 18 no. 6, (2016) 063026, arXiv:1412.8462 [quant-ph].
https://doi.org/10.1088/1367-2630/18/6/063026
arXiv:1412.8462

[39] P. A. Guérin and Č. Brukner, ``Observer-dependent locality of quantum events,'' New J. Phys. 20, 103031 (2018), arXiv:1805.12429 [quant-ph].
https://doi.org/10.1088/1367-2630/aae742
arXiv:1805.12429

[40] O. Oreshkov, F. Costa, and Č. Brukner, ``Quantum correlations with no causal order,'' Nature communications 3 (2012) 1092, arXiv:1105.4464 [quant-ph].
https://doi.org/10.1038/ncomms2076
arXiv:1105.4464

[41] L. Hardy, ``The Construction Interpretation: Conceptual Roads to Quantum Gravity,'' arXiv:1807.10980 [quant-ph].
arXiv:1807.10980

[42] P. A. Höhn, ``Reflections on the information paradigm in quantum and gravitational physics,'' J. Phys. Conf. Ser. 880 no. 1, (2017) 012014, arXiv:1706.06882 [hep-th].
https://doi.org/10.1088/1742-6596/880/1/012014
arXiv:1706.06882

[43] P. A. Dirac, Lectures on Quantum Mechanics. Yeshiva University Press, 1964.
https://doi.org/10.1142/6093

[44] M. Henneaux and C. Teitelboim, Quantization of Gauge Systems. Princeton University Press, 1992.

[45] C. Rovelli, ``Why Gauge?,'' Found. Phys. 44 no. 1, (2014) 91–104, arXiv:1308.5599 [hep-th].
https://doi.org/10.1007/s10701-013-9768-7
arXiv:1308.5599

[46] H. Gomes, F. Hopfmüller, and A. Riello, ``A unified geometric framework for boundary charges and dressings: non-Abelian theory and matter,'' Nuclear Physics B 941 (2019) 249-315, arXiv:1808.02074 [hep-th].
https://doi.org/10.1016/j.nuclphysb.2019.02.020
arXiv:1808.02074

[47] V. Guillemin and S. Sternberg, ``Geometric quantization and multiplicities of group representations,'' Inventiones mathematicae 67 no. 3, (1982) 515–538.
https://doi.org/10.1007/BF01398934

[48] Y. Tian and W. Zhang, ``An analytic proof of the geometric quantization conjecture of guillemin-sternberg,'' Inventiones mathematicae 132 no. 2, (1998) 229–259.
https://doi.org/10.1007/s002220050223

[49] P. Hochs and N. Landsman, ``The guillemin–sternberg conjecture for noncompact groups and spaces,'' Journal of K-theory 1 no. 3, (2008) 473–533, arXiv:math-ph/0512022.
https://doi.org/10.1017/is008001002jkt022
arXiv:math-ph/0512022

[50] M. J. Gotay, ``Constraints, reduction, and quantization,'' Journal of mathematical physics 27 no. 8, (1986) 2051–2066.
https://doi.org/10.1063/1.527026

[51] A. Ashtekar and G. t. Horowitz, ``On the canonical approach to quantum gravity,'' Phys. Rev. D26 (1982) 3342–3353.
https://doi.org/10.1103/PhysRevD.26.3342

[52] K. Kuchař, ``Covariant factor ordering of gauge systems,'' Physical Review D 34 no. 10, (1986) 3044.
https://doi.org/10.1103/physrevd.34.3044

[53] A. Ashtekar, Lectures on Nonperturbative Canonical Gravity, No. 6 in Advances series in astrophysics and cosmology. World Scientific, 1991.
https://doi.org/10.1142/1321

[54] K. Schleich, ``Is reduced phase space quantization equivalent to Dirac quantization?,'' Class. Quant. Grav. 7 (1990) 1529–1538.
https://doi.org/10.1088/0264-9381/7/8/028

[55] G. Kunstatter, ``Dirac versus reduced quantization: A Geometrical approach,'' Class. Quant. Grav. 9 (1992) 1469–1486.
https://doi.org/10.1088/0264-9381/9/6/005

[56] P. Hajicek and K. V. Kuchar, ``Constraint quantization of parametrized relativistic gauge systems in curved space-times,'' Phys. Rev. D41 (1990) 1091–1104.
https://doi.org/10.1103/PhysRevD.41.1091

[57] J. D. Romano and R. S. Tate, ``Dirac Versus Reduced Space Quantization of Simple Constrained Systems,'' Class. Quant. Grav. 6 (1989) 1487.
https://doi.org/10.1088/0264-9381/6/10/017

[58] R. Loll, ``Noncommutativity of constraining and quantizing: A U(1) gauge model,'' Phys. Rev. D41 (1990) 3785–3791.
https://doi.org/10.1103/PhysRevD.41.3785

[59] M. S. Plyushchay and A. V. Razumov, ``Dirac versus reduced phase space quantization for systems admitting no gauge conditions,'' International Journal of Modern Physics A 11 no. 08, (1996) 1427–1462, arXiv:hep-th/9306017.
https://doi.org/10.1142/S0217751X96000663
arXiv:hep-th/9306017

[60] P. A. Höhn, ``Toolbox for reconstructing quantum theory from rules on information acquisition,'' Quantum 1 no. 38, (2017) , arXiv:1412.8323 [quant-ph].
https://doi.org/10.22331/q-2017-12-14-38
arXiv:1412.8323

[61] C. Rovelli, ``Relational quantum mechanics,'' Int.J.Theor.Phys. 35 (1996) 1637–1678, arXiv:quant-ph/9609002 [quant-ph].
https://doi.org/10.1007/BF02302261
arXiv:quant-ph/9609002

[62] C. Rovelli, ``Space is blue and birds fly through it,'' Phil. Trans. R. Soc. A 376 no. 2123, (2018) 20170312, arXiv:1712.02894 [physics.hist-ph].
https://doi.org/10.1098/rsta.2017.0312
arXiv:1712.02894

[63] H. Gomes, S. Gryb, and T. Koslowski, ``Einstein gravity as a 3D conformally invariant theory,'' Class.Quant.Grav. 28 (2011) 045005, arXiv:1010.2481 [gr-qc].
https://doi.org/10.1088/0264-9381/28/4/045005
arXiv:1010.2481

[64] H. Gomes and T. Koslowski, ``The Link between General Relativity and Shape Dynamics,'' Class. Quant. Grav. 29 (2012) 075009, arXiv:1101.5974 [gr-qc].
https://doi.org/10.1088/0264-9381/29/7/075009
arXiv:1101.5974

[65] P. A. Höhn, M. P. Müller, C. Pfeifer, and D. Rätzel, ``A local quantum Mach principle and the metricity of spacetime,'' arXiv:1811.02555 [gr-qc].
arXiv:1811.02555

[66] J. Barbour, T. Koslowski, and F. Mercati, ``Identification of a gravitational arrow of time,'' Phys. Rev. Lett. 113 no. 18, (2014) 181101, arXiv:1409.0917 [gr-qc].
https://doi.org/10.1103/PhysRevLett.113.181101
arXiv:1409.0917

[67] J. Barbour, T. Koslowski, and F. Mercati, ``Entropy and the Typicality of Universes,'' arXiv:1507.06498 [gr-qc].
arXiv:1507.06498

[68] P. Hájíček, ``Origin of nonunitarity in quantum gravity,'' Phys.Rev. D34 (1986) 1040.
https://doi.org/10.1103/PhysRevD.34.1040

[69] A. Kempf and J. R. Klauder, ``On the implementation of constraints through projection operators,'' J. Phys. A34 (2001) 1019–1036, arXiv:quant-ph/0009072 [quant-ph].
https://doi.org/10.1088/0305-4470/34/5/307
arXiv:quant-ph/0009072

[70] D. Marolf, ``Refined algebraic quantization: Systems with a single constraint,'' arXiv:gr-qc/9508015 [gr-qc].
arXiv:gr-qc/9508015

[71] D. Marolf, ``Group averaging and refined algebraic quantization: Where are we now?,'' arXiv:gr-qc/0011112 [gr-qc].
arXiv:gr-qc/0011112

[72] L. D. Faddeev and V. N. Popov, ``Feynman Diagrams for the Yang-Mills Field,'' Phys. Lett. B 25 (1967) 29–30.
https://doi.org/10.1016/0370-2693(67)90067-6

[73] E. S. Fradkin and G. A. Vilkovisky, ``Quantization of relativistic systems with constraints,'' Phys. Lett. 55B (1975) 224–226.
https://doi.org/10.1016/0370-2693(75)90448-7

[74] I. A. Batalin and G. A. Vilkovisky, ``Relativistic S Matrix of Dynamical Systems with Boson and Fermion Constraints,'' Phys. Lett. 69B (1977) 309–312.
https://doi.org/10.1016/0370-2693(77)90553-6

[75] E. S. Fradkin and T. E. Fradkina, ``Quantization of Relativistic Systems with Boson and Fermion First and Second Class Constraints,'' Phys. Lett. 72B (1978) 343–348.
https://doi.org/10.1016/0370-2693(78)90135-1

[76] B. Dittrich and P. A. Höhn, ``Canonical simplicial gravity,'' Class.Quant.Grav. 29 (2012) 115009, arXiv:1108.1974 [gr-qc].
https://doi.org/10.1088/0264-9381/29/11/115009
arXiv:1108.1974

[77] B. Dittrich and P. A. Höhn, ``Constraint analysis for variational discrete systems,'' J. Math. Phys. 54 (2013) 093505, arXiv:1303.4294 [math-ph].
https://doi.org/10.1063/1.4818895
arXiv:1303.4294

[78] P. A. Höhn, ``Classification of constraints and degrees of freedom for quadratic discrete actions,'' J.Math.Phys. 55 (2014) 113506, arXiv:1407.6641 [math-ph].
https://doi.org/10.1063/1.4900926
arXiv:1407.6641

[79] P. A. Höhn, ``Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves,'' Phys. Rev. D91 no. 12, (2015) 124034, arXiv:1411.5672 [gr-qc].
https://doi.org/10.1103/PhysRevD.91.124034
arXiv:1411.5672

[80] P. A. Höhn, ``Quantization of systems with temporally varying discretization II: Local evolution moves,'' J.Math.Phys. 55 (2014) 103507, arXiv:1401.7731 [gr-qc].
https://doi.org/10.1063/1.4898764
arXiv:1401.7731

[81] D. N. Page and W. K. Wootters, ``Evolution without evolution: Dynamics described by stationary observables,'' Phys. Rev. D27 (1983) 2885.
https://doi.org/10.1103/PhysRevD.27.2885

[82] F. Giacomini, E. Castro-Ruiz, and Č. Brukner, ``Relativistic quantum reference frames: the operational meaning of spin,'' Physical review letters 123 no. 9, (2019) 090404, arXiv:1811.08228 [quant-ph].
https://doi.org/10.1103/PhysRevLett.123.090404
arXiv:1811.08228

[83] E. P. Wigner, ``Remarks on the mind-body question,'' in Philosophical reflections and syntheses, pp. 247–260. Springer, 1995.
https://doi.org/10.1007/978-3-642-78374-6_20

[84] D. Deutsch, ``Quantum theory as a universal physical theory,'' International Journal of Theoretical Physics 24 no. 1, (1985) 1–41.
https://doi.org/10.1007/BF00670071

[85] Č. Brukner, ``On the quantum measurement problem,'' in Quantum [Un] Speakables II, pp. 95–117. Springer, 2017, arXiv:1507.05255 [quant-ph].
https://doi.org/10.1007/978-3-319-38987-5_5
arXiv:1507.05255

[86] D. Frauchiger and R. Renner, ``Quantum theory cannot consistently describe the use of itself,'' Nature Communications 9 no. 3711, (2018) , arXiv:1604.07422 [quant-ph].
https://doi.org/10.1038/s41467-018-05739-8
arXiv:1604.07422

[87] P. A. Höhn and C. S. P. Wever, ``Quantum theory from questions,'' Phys. Rev. A95 no. 1, (2017) 012102, arXiv:1511.01130 [quant-ph].
https://doi.org/10.1103/PhysRevA.95.012102
arXiv:1511.01130

[88] P. A. Höhn, ``Quantum theory from rules on information acquisition,'' Entropy 19 (2017) 98, arXiv:1612.06849 [quant-ph].
https://doi.org/10.3390/e19030098
arXiv:1612.06849

[89] L. Hardy, ``Quantum theory from five reasonable axioms,'' arXiv:quant-ph/0101012 [quant-ph].
arXiv:quant-ph/0101012

[90] B. Dakic and C. Brukner, ``Quantum theory and beyond: Is entanglement special?,'' Deep Beauty: Understanding the Quantum World through Mathematical Innovation, Ed. H. Halvorson (Cambridge University Press, 2011) 365-392 (11, 2009) , arXiv:0911.0695 [quant-ph].
https://doi.org/10.1017/CBO9780511976971.011
arXiv:0911.0695

[91] L. Masanes and M. P. Müller, ``A derivation of quantum theory from physical requirements,'' New Journal of Physics 13 no. 6, (2011) 063001, arXiv:1004.1483 [quant-ph].
arXiv:1004.1483

[92] G. Chiribella, G. M. D'Ariano, and P. Perinotti, ``Informational derivation of quantum theory,'' Physical Review A 84 no. 1, (2011) 012311, arXiv:1011.6451 [quant-ph].
https://doi.org/10.1103/PhysRevA.84.012311
arXiv:1011.6451

[93] H. Barnum, M. P. Müller, and C. Ududec, ``Higher-order interference and single-system postulates characterizing quantum theory,'', New Journal of Physics 16, (2011) 123029, arXiv:1403.4147 [quant-ph].
https://doi.org/10.1088/1367-2630/16/12/123029
arXiv:1403.4147

[94] P. Goyal, ``From information geometry to quantum theory,'' New Journal of Physics 12 no. 2, (2010) 023012, arXiv:0805.2770 [quant-ph].
https://doi.org/10.1088/1367-2630/12/2/023012
arXiv:0805.2770

[95] M. P. Müller, ``Law without law: from observer states to physics via algorithmic information theory,'' arXiv:1712.01826 [quant-ph].
arXiv:1712.01826

[96] M. P. Müller, ``Could the physical world be emergent instead of fundamental, and why should we ask? (short version),'' arXiv:1712.01816 [quant-ph].
arXiv:1712.01816

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[6] Wolfgang Wieland, "Barnich–Troessaert bracket as a Dirac bracket on the covariant phase space", Classical and Quantum Gravity 39 2, 025016 (2022).

[7] Julian De Vuyst, Stefan Eccles, Philipp A. Höhn, and Josh Kirklin, "Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy", Journal of High Energy Physics 2025 7, 63 (2025).

[8] Philipp A. Höhn, Alexander R. H. Smith, and Maximilian P. E. Lock, "Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings", Frontiers in Physics 9, 587083 (2021).

[9] Emily Adlam, "How Do We Observe Relational Observables?", Journal for General Philosophy of Science 57 2, 285 (2026).

[10] Martin Bojowald, Luis Martínez, and Garrett Wendel, "Relational evolution with oscillating clocks", Physical Review D 105 10, 106020 (2022).

[11] Viktoria Kabel, Anne-Catherine de la Hamette, Esteban Castro-Ruiz, and Časlav Brukner, "Quantum conformal symmetries for spacetimes in superposition", Quantum 8, 1547 (2024).

[12] Carlo Cepollaro, Ali Akil, Paweł Cieśliński, Anne-Catherine de la Hamette, and Časlav Brukner, "Sum of Entanglement and Subsystem Coherence Is Invariant under Quantum Reference Frame Transformations", Physical Review Letters 135 1, 010201 (2025).

[13] Rhea Alexander, Si Gvirtz-Chen, and David Jennings, "Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system", New Journal of Physics 24 5, 053023 (2022).

[14] H. Hadi and Amin Rezaei Akbarieh, "Dynamical non-locality in the near-horizon region of a black hole with quantum time", Physics Letters B 858, 139049 (2024).

[15] Eduardo A. B. Oliveira and André G. S. Landulfo, "Spacetime-covariant approach to inertial and accelerated quantum clocks in first quantization", Physical Review D 113 4, 045018 (2026).

[16] M. F. Savi and R. M. Angelo, "Quantum resource covariance", Physical Review A 103 2, 022220 (2021).

[17] Martin Bojowald and Luis Martínez, "Large effects from quantum reference frames", Journal of Physics A: Mathematical and Theoretical 58 27, 275302 (2025).

[18] Wolfgang Wieland, "Quantum geometry of the light cone: Fock representation and spectrum of radiated power", Classical and Quantum Gravity 42 19, 195006 (2025).

[19] Achim Kempf, "Replacing the Notion of Spacetime Distance by the Notion of Correlation", Frontiers in Physics 9, 655857 (2021).

[20] Marius Krumm, Philipp A. Höhn, and Markus P. Müller, "Quantum reference frame transformations as symmetries and the paradox of the third particle", Quantum 5, 530 (2021).

[21] Guilhem Doat and Augustin Vanrietvelde, "What can we do in a symmetry-constrained perspective? The importance of the total charge's status in quantum reference frame frameworks", Quantum 10, 2126 (2026).

[22] Jianhao M. Yang, "Path integral implementation of relational quantum mechanics", Scientific Reports 11 1, 8613 (2021).

[23] Isha Kotecha, Springer Theses 167 (2022) ISBN:978-3-030-90968-0.

[24] Esteban Castro-Ruiz and Ognyan Oreshkov, "Relative subsystems and quantum reference frame transformations", Communications Physics 8 1, 187 (2025).

[25] T. Rick Perche and Eduardo Martín-Martínez, "Geometry of spacetime from quantum measurements", Physical Review D 105 6, 066011 (2022).

[26] Leonardo Chataignier, "Construction of quantum Dirac observables and the emergence of WKB time", Physical Review D 101 8, 086001 (2020).

[27] Yuxiang Yang, Yin Mo, Joseph M. Renes, Giulio Chiribella, and Mischa P. Woods, "Optimal universal quantum error correction via bounded reference frames", Physical Review Research 4 2, 023107 (2022).

[28] Martin Bojowald and Artur Tsobanjan, "Algebraic Properties of Quantum Reference Frames: Does Time Fluctuate?", Quantum Reports 5 1, 22 (2022).

[29] Gonçalo Araujo-Regado, Philipp A. Höhn, Francesco Sartini, and Bilyana Tomova, "Soft edges: the many links between soft and edge modes", Journal of High Energy Physics 2025 7, 180 (2025).

[30] Adam Dukehart and David Mattingly, "Energy cost of localization of relational quantum information", Physical Review D 107 12, 126020 (2023).

[31] Emily Adlam, "Moderate Physical Perspectivalism", Philosophy of Science 92 3, 624 (2025).

[32] Christian de Ronde and César Massri, "Relational quantum entanglement beyond non-separable and contextual relativism", Studies in History and Philosophy of Science 97, 68 (2023).

[33] Andrzej Góźdź, Marek Góźdź, and Aleksandra Pȩdrak, "Quantum Time and Quantum Evolution", Universe 9 6, 256 (2023).

[34] Luis Martinez, Martin Bojowald, and Garrett Wendel, "Freeze-free cosmological evolution with a nonmonotonic internal clock", Physical Review D 108 8, 086001 (2023).

[35] Wolfgang Wieland, "Null infinity as an open Hamiltonian system", Journal of High Energy Physics 2021 4, 95 (2021).

[36] Eric G. Cavalcanti, "The View from a Wigner Bubble", Foundations of Physics 51 2, 39 (2021).

[37] Ismael L. Paiva, Pedro R. Dieguez, Renato M. Angelo, and Eliahu Cohen, "Coherence and realism in the Aharonov-Bohm effect", Physical Review A 107 3, 032213 (2023).

[38] Shadi Ali Ahmad, Thomas D. Galley, Philipp A. Höhn, Maximilian P. E. Lock, and Alexander R. H. Smith, "Quantum Relativity of Subsystems", Physical Review Letters 128 17, 170401 (2022).

[39] Leonardo Chataignier, Springer Theses 69 (2022) ISBN:978-3-030-94447-6.

[40] Sylvain Carrozza, Stefan Eccles, and Philipp A. Hoehn, "Edge modes as dynamical frames: charges from post-selection in generally covariant theories", SciPost Physics 17 2, 048 (2024).

[41] Anne-Catherine de la Hamette, Viktoria Kabel, Marios Christodoulou, and Časlav Brukner, "Indefinite Causal Order and Quantum Coordinates", Physical Review Letters 135 14, 141402 (2025).

[42] M.J. Luo, "Quantum mechanics relative to a quantum reference system: A relative state approach", Annals of Physics 489, 170431 (2026).

[43] Daan W. Janssen, "Quantum reference frames for spacetime symmetries and large gauge transformations", Journal of Physics: Conference Series 3177 1, 012137 (2026).

[44] Achim Kempf, "The metric from energy-momentum non-conservation: Generalizing Noether and completing spectral geometry", Journal of Physics: Conference Series 3017 1, 012003 (2025).

[45] Laurent Freidel, Marc Geiller, and Wolfgang Wieland, Handbook of Quantum Gravity 4185 (2024) ISBN:978-981-99-7680-5.

[46] Anderson A. Tomaz, Rafael S. Mattos, and Mario Barbatti, "The quantum measurement problem: a review of recent trends", Philosophical Magazine 1 (2025).

[47] Simone Rijavec, "Conditions for unitarity in timeless quantum theory", Physical Review D 114 4, 045012 (2026).

[48] Anne-Catherine de la Hamette, Viktoria Kabel, Esteban Castro-Ruiz, and Časlav Brukner, "Quantum reference frames for an indefinite metric", Communications Physics 6 1, 231 (2023).

[49] Steffen Gielen, "Frozen formalism and canonical quantization in group field theory", Physical Review D 104 10, 106011 (2021).

[50] Sergio E. Aguilar-Gutierrez, "Symmetry sectors in chord space and relational holography in the DSSYK. Lessons from branes, wormholes, and de Sitter space", Journal of High Energy Physics 2025 10, 44 (2025).

[51] Otto C W Kong, "On the symmetry of Special Quantum Relativity", Classical and Quantum Gravity 42 11, 115007 (2025).

[52] Tommaso Favalli, Springer Theses 13 (2024) ISBN:978-3-031-52351-9.

[53] Julian Wechs and Ognyan Oreshkov, "Subsystem Decompositions of Quantum Evolutions and Transformations between Causal Perspectives", Physical Review Letters 135 19, 190201 (2025).

[54] Leonardo Chataignier, "Relational observables, reference frames, and conditional probabilities", Physical Review D 103 2, 026013 (2021).

[55] G Amelino-Camelia, V D’Esposito, G Fabiano, D Frattulillo, P A Höhn, and F Mercati, "Quantum Euler angles and agency-dependent space-time", Progress of Theoretical and Experimental Physics 2024 3, 033A01 (2024).

[56] Alexander Yu Kamenshchik, Jeinny Nallely Pérez Rodríguez, and Tereza Vardanyan, "Time and Evolution in Quantum and Classical Cosmology", Universe 7 7, 219 (2021).

[57] Leonardo Chataignier, "Beyond semiclassical time", Zeitschrift für Naturforschung A 77 8, 805 (2022).

[58] Carlo Cepollaro and Flaminia Giacomini, "Quantum generalisation of Einstein’s equivalence principle can be verified with entangled clocks as quantum reference frames", Classical and Quantum Gravity 41 18, 185009 (2024).

[59] Eugenio Bianchi, Pietro Dona, and Rishabh Kumar, "Non-Abelian symmetry-resolved entanglement entropy", SciPost Physics 17 5, 127 (2024).

[60] Renata Ferrero, "Asymptotic safety and canonical quantum gravity", International Journal of Modern Physics A 41 03, 2530023 (2026).

[61] Pierre Martin-Dussaud, "Relational Structures of Fundamental Theories", Foundations of Physics 51 1, 24 (2021).

[62] Julian De Vuyst, Stefan Eccles, Philipp A. Höhn, and Josh Kirklin, "Gravitational entropy is observer-dependent", Journal of High Energy Physics 2025 7, 146 (2025).

[63] Sergio E. Aguilar-Gutierrez, "Evolution with(out) time: relational holography & BPS complexity growth in $$ \mathcal{N} $$ = 2 double-scaled SYK", Journal of High Energy Physics 2026 2, 229 (2026).

[64] Aleksandra Dimić, Marko Milivojević, Dragoljub Gočanin, Natália S. Móller, and Časlav Brukner, "Simulating Indefinite Causal Order With Rindler Observers", Frontiers in Physics 8, 525333 (2020).

[65] Alexander Bonilla, Suresh Kumar, Rafael C Nunes, and Supriya Pan, "Reconstruction of the dark sectors’ interaction: A model-independent inference and forecast from GW standard sirens", Monthly Notices of the Royal Astronomical Society 512 3, 4231 (2022).

[66] Martin Bojowald and Artur Tsobanjan, "Quantization of Dynamical Symplectic Reduction", Communications in Mathematical Physics 382 1, 547 (2021).

[67] Philipp A. Höhn, Marius Krumm, and Markus P. Müller, "Internal quantum reference frames for finite Abelian groups", Journal of Mathematical Physics 63 11, 112207 (2022).

[68] Veronika Baumann, Flavio Del Santo, Alexander R. H. Smith, Flaminia Giacomini, Esteban Castro-Ruiz, and Caslav Brukner, "Generalized probability rules from a timeless formulation of Wigner's friend scenarios", Quantum 5, 524 (2021).

[69] Sergio E. Aguilar-Gutierrez, "Cosmological entanglement entropy from the von Neumann algebra of double-scaled SYK & its connection with Krylov complexity", Journal of High Energy Physics 2026 5, 80 (2026).

[70] Matthew J. Lake, "Towards a Quantum Erlangen Program", Universe 12 3, 84 (2026).

[71] Viktoria Kabel, Časlav Brukner, and Wolfgang Wieland, "Quantum reference frames at the boundary of spacetime", Physical Review D 108 10, 106022 (2023).

[72] Flaminia Giacomini, "Spacetime Quantum Reference Frames and superpositions of proper times", Quantum 5, 508 (2021).

[73] Elliott Tammaro, H. Angle, and E. Mbadu, "Considering a superposition of classical reference frames", Journal of Mathematical Physics 64 12, 122102 (2023).

[74] Michael Suleymanov, Ismael L. Paiva, and Eliahu Cohen, "Nonrelativistic spatiotemporal quantum reference frames", Physical Review A 109 3, 032205 (2024).

[75] Garrett Wendel, Luis Martínez, and Martin Bojowald, "Physical Implications of a Fundamental Period of Time", Physical Review Letters 124 24, 241301 (2020).

[76] Henrique Gomes, Simon Langenscheidt, and Daniele Oriti, Open Systems: Physics, Metaphysics, and Methodology 147 (2026) ISBN:9780198929246.

[77] Leon Loveridge, "A relational perspective on the Wigner-Araki-Yanase theorem", Journal of Physics: Conference Series 1638 1, 012009 (2020).

[78] Salvatore Capozziello and Carmen Ferrara, "The equivalence principle as a Noether symmetry", International Journal of Geometric Methods in Modern Physics 21 10, 2440014 (2024).

[79] Alexander R. H. Smith and Mehdi Ahmadi, "Quantum clocks observe classical and quantum time dilation", Nature Communications 11 1, 5360 (2020).

[80] Anne-Catherine de la Hamette, Stefan L. Ludescher, and Markus P. Müller, "Entanglement-Asymmetry Correspondence for Internal Quantum Reference Frames", Physical Review Letters 129 26, 260404 (2022).

[81] Koji Yamaguchi, Yosuke Mitsuhashi, Tomohiro Shitara, and Hiroyasu Tajima, "Quantum Geometric Tensor Determines the Pure-State I.I.D. Conversion Rate in the Resource Theory of Asymmetry for Any Compact Lie Group", Physical Review X 16 3, 031028 (2026).

[82] Steffen Gielen and Axel Polaczek, "Hamiltonian group field theory with multiple scalar matter fields", Physical Review D 103 8, 086011 (2021).

[83] Vittorio D'Esposito, Giuseppe Fabiano, Domenico Frattulillo, and Flavio Mercati, "Doubly Quantum Mechanics", Quantum 9, 1721 (2025).

[84] Christopher J. Fewster, Daan W. Janssen, Leon Deryck Loveridge, Kasia Rejzner, and James Waldron, "Quantum Reference Frames, Measurement Schemes and the Type of Local Algebras in Quantum Field Theory", Communications in Mathematical Physics 406 1, 19 (2025).

[85] Włodzimierz Piechocki and Tim Schmitz, "Quantum Oppenheimer-Snyder model", Physical Review D 102 4, 046004 (2020).

[86] Marion Mikusch, Luis C. Barbado, and Časlav Brukner, "Transformation of spin in quantum reference frames", Physical Review Research 3 4, 043138 (2021).

[87] Andrea Calcinari and Steffen Gielen, "Relational dynamics and Page-Wootters formalism in group field theory", Quantum 9, 1610 (2025).

[88] Tommaso Favalli, Springer Theses 1 (2024) ISBN:978-3-031-52351-9.

[89] Steffen Gielen and Lucía Menéndez-Pidal, "Singularity resolution depends on the clock", Classical and Quantum Gravity 37 20, 205018 (2020).

[90] Максим Чурилов, "Quantum Reference Frames Beyond Ideality: Complete-Order Quotients, Resource Lattices, and Certified Transformations", (2026).

[91] Esteban Castro-Ruiz, Flaminia Giacomini, Alessio Belenchia, and Časlav Brukner, "Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems", Nature Communications 11 1, 2672 (2020).

[92] Chris Overstreet, Joseph Curti, Minjeong Kim, Peter Asenbaum, Mark A. Kasevich, and Flaminia Giacomini, "Inference of gravitational field superposition from quantum measurements", Physical Review D 108 8, 084038 (2023).

[93] Ivan Agullo, Anzhong Wang, and Edward Wilson-Ewing, Handbook of Quantum Gravity 1 (2023) ISBN:978-981-19-3079-9.

[94] M. Basil Altaie, Daniel Hodgson, and Almut Beige, "Time and Quantum Clocks: A Review of Recent Developments", Frontiers in Physics 10, 897305 (2022).

[95] Kristina Giesel, Viktoria Kabel, and Wolfgang Wieland, "Linking edge modes and geometrical clocks in linearized gravity", Physical Review D 112 6, 064063 (2025).

[96] Tommaso Favalli, Springer Theses 89 (2024) ISBN:978-3-031-52351-9.

[97] Luis C Barbado and Časlav Brukner, Open Systems: Physics, Metaphysics, and Methodology 174 (2026) ISBN:9780198929246.

[98] Miguel Jorquera Riera and Leon Loveridge, "Uncertainty relations relative to phase-space quantum reference frames", Physical Review A 111 6, L060201 (2025).

[99] Isha Kotecha, Springer Theses 61 (2022) ISBN:978-3-030-90968-0.

[100] Luca Apadula, Esteban Castro-Ruiz, and Časlav Brukner, "Quantum Reference Frames for Lorentz Symmetry", Quantum 8, 1440 (2024).

[101] Luca Ciambelli, Laurent Freidel, and Robert G. Leigh, "Quantum null geometry and gravity", Journal of High Energy Physics 2024 12, 28 (2024).

[102] Leonardo Chataignier, Philipp A Höhn, Maximilian P E Lock, and Fabio M Mele, "Relational dynamics with periodic clocks", New Journal of Physics 28 3, 034504 (2026).

[103] Anne-Catherine de la Hamette and Thomas D. Galley, "Quantum reference frames for general symmetry groups", Quantum 4, 367 (2020).

[104] Nikola Paunković and Marko Vojinović, "Equivalence Principle in Classical and Quantum Gravity", Universe 8 11, 598 (2022).

[105] Flaminia Giacomini and Achim Kempf, "Second-quantized Unruh-DeWitt detectors and their quantum reference frame transformations", Physical Review D 105 12, 125001 (2022).

[106] Martin Bojowald, "Noncovariance of the dressed-metric approach in loop quantum cosmology", Physical Review D 102 2, 023532 (2020).

[107] Augustin Vanrietvelde, Philipp A. Höhn, and Flaminia Giacomini, "Switching quantum reference frames in the N-body problem and the absence of global relational perspectives", Quantum 7, 1088 (2023).

[108] Angel Ballesteros, Diego Fernandez-Silvestre, Flaminia Giacomini, and Giulia Gubitosi, "Quantum Galilei group as quantum reference frame transformations", Quantum 9, 1935 (2025).

[109] Ronak M. Soni, "A type I approximation of the crossed product", Journal of High Energy Physics 2024 1, 123 (2024).

[110] Emily Adlam, "Watching the Clocks: Interpreting the Page–Wootters Formalism and the Internal Quantum Reference Frame Programme", Foundations of Physics 52 5, 99 (2022).

[111] Josh Kirklin, "Generalised second law beyond the semiclassical regime", Journal of High Energy Physics 2025 7, 192 (2025).

[112] Jibril Ben Achour, Dario Benedetti, Martin Bojowald, Robert Brandenberger, Salvatore Butera, Renata Ferrero, Flaminia Giacomini, Kristina Giesel, Christophe Goeller, Tobias Haas, Philipp A. Höhn, Joshua Kirklin, Luca Marchetti, Daniele Oriti, Roberto Percacci, Antonio D. Pereira, Andreas G. A. Pithis, Mairi Sakellariadou, Sebastian Steinhaus, and Johannes Thürigen, "Quantum gravity, hydrodynamics and emergent cosmology: a collection of perspectives", General Relativity and Gravitation 57 1, 2 (2025).

[113] T. Favalli and A. Smerzi, "A model of quantum spacetime", AVS Quantum Science 4 4, 044403 (2022).

[114] Henrique A.R. Knopki and Renato M. Angelo, "Searching for a physical description relative to a quantum system", Physics Letters A 560, 130932 (2025).

[115] Pierre Martin-Dussaud, "Perspective on: Switching Quantum Reference Frames for Quantum Measurement", Quantum Views 4, 40 (2020).

[116] Tommaso Favalli and Augusto Smerzi, "Peaceful coexistence of thermal equilibrium and the emergence of time", Physical Review D 105 2, 023525 (2022).

[117] Steffen Gielen and Axel Polaczek, "Generalised effective cosmology from group field theory", Classical and Quantum Gravity 37 16, 165004 (2020).

[118] Alireza Tavanfar, Sahar Alipour, and Ali T. Rezakhani, "Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories", Universe 11 5, 162 (2025).

[119] Leonardo Chataignier and Manuel Krämer, "Unitarity of quantum-gravitational corrections to primordial fluctuations in the Born-Oppenheimer approach", Physical Review D 103 6, 066005 (2021).

[120] Leonardo Chataignier, Springer Theses 185 (2022) ISBN:978-3-030-94447-6.

[121] Titouan Carette, Jan Glowacki, and Leon Loveridge, "Operational Quantum Reference Frame Transformations", Quantum 9, 1680 (2025).

[122] Viktoria Kabel, Anne-Catherine de la Hamette, Luca Apadula, Carlo Cepollaro, Henrique Gomes, Jeremy Butterfield, and Časlav Brukner, "Quantum coordinates, localisation of events, and the quantum hole argument", Communications Physics 8 1, 185 (2025).

[123] Emily Adlam, "Relational observables, quiddities, and structural realism", Synthese 206 2, 104 (2025).

[124] Rain Lenny, Amit Te’eni, Michael Suleymanov, and Eliahu Cohen, "Relativistic independence and multipartite quantum correlations", The European Physical Journal Special Topics 235 11, 2835 (2026).

[125] Viktor Zelezny, "Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structure", Quantum 7, 1098 (2023).

[126] Flaminia Giacomini and Časlav Brukner, "Quantum superposition of spacetimes obeys Einstein's equivalence principle", AVS Quantum Science 4 1, 015601 (2022).

[127] Philipp A. Höhn, Alexander R. H. Smith, and Maximilian P. E. Lock, "Trinity of relational quantum dynamics", Physical Review D 104 6, 066001 (2021).

[128] Michael Suleymanov and Eliahu Cohen, "Quantum frames of reference and the relational flow of time", The European Physical Journal Special Topics 232 20-22, 3325 (2023).

[129] Ivan Agullo, Anzhong Wang, and Edward Wilson-Ewing, Handbook of Quantum Gravity 4039 (2024) ISBN:978-981-99-7680-5.

[130] Jianhao M. Yang, "Switching Quantum Reference Frames for Quantum Measurement", Quantum 4, 283 (2020).

[131] Jan Głowacki, Leon Loveridge, and James Waldron, "Quantum Reference Frames on Finite Homogeneous Spaces", International Journal of Theoretical Physics 63 5, 137 (2024).

[132] Julian De Vuyst, Philipp A. Hoehn, and Artur Tsobanjan, "On the relation between perspective-neutral, algebraic, and effective quantum reference frames", Quantum 10, 2196 (2026).

[133] Philipp A. Höhn, Andrea Russo, and Alexander R. H. Smith, "Matter relative to quantum hypersurfaces", Physical Review D 109 10, 105011 (2024).

[134] Christophe Goeller, Philipp A. Hoehn, and Josh Kirklin, "Diffeomorphism-invariant observables and dynamical frames in gravity: reconciling bulk locality with general covariance", arXiv:2206.01193, (2022).

[135] Anderson A. Tomaz, Rafael S. Mattos, and Mario Barbatti, "The Quantum Measurement Problem: A Review of Recent Trends", arXiv:2502.19278, (2025).

[136] Flaminia Giacomini, Esteban Castro-Ruiz, and Časlav Brukner, "Relativistic Quantum Reference Frames: The Operational Meaning of Spin", Physical Review Letters 123 9, 090404 (2019).

[137] Jianhao M. Yang, "Quantum Mechanics from Relational Properties, Part III: Path Integral Implementation", arXiv:1807.01583, (2018).

[138] Philipp A. Hoehn, Isha Kotecha, and Fabio M. Mele, "Quantum Frame Relativity of Subsystems, Correlations and Thermodynamics", arXiv:2308.09131, (2023).

[139] Philipp A. Höhn, "Switching Internal Times and a New Perspective on the `Wave Function of the Universe'", Universe 5 5, 116 (2019).

[140] Ted Jacobson and Phuc Nguyen, "Diffeomorphism invariance and the black hole information paradox", Physical Review D 100 4, 046002 (2019).

[141] Alexander F. Jercher, Luca Marchetti, and Andreas G. A. Pithis, "Scalar cosmological perturbations from quantum gravitational entanglement", Classical and Quantum Gravity 41 18, 18LT01 (2024).

[142] Matthew J. Lake and Marek Miller, "Quantum reference frames, revisited", arXiv:2312.03811, (2023).

[143] Sylvain Carrozza, Aidan Chatwin-Davies, Philipp A. Hoehn, and Fabio M. Mele, "A correspondence between quantum error correcting codes and quantum reference frames", arXiv:2412.15317, (2024).

[144] Laurent Freidel, Marc Geiller, and Wolfgang Wieland, "Corner symmetry and quantum geometry", arXiv:2302.12799, (2023).

[145] Philipp A Hoehn and Augustin Vanrietvelde, "How to switch between relational quantum clocks", arXiv:1810.04153, (2018).

[146] Aldo Riello, "Edge modes without edge modes", arXiv:2104.10182, (2021).

[147] Guilherme Franzmann, "To be or not to be, but where?", arXiv:2405.21031, (2024).

[148] Goncalo Araujo-Regado, Philipp A. Hoehn, and Francesco Sartini, "Relational entanglement entropies and quantum reference frames in gauge theories", arXiv:2506.23459, (2025).

[149] Allic Sivaramakrishnan, "Correlators of Worldline Proper Length", arXiv:2406.17205, (2024).

[150] Lucien Hardy, "Implementation of the Quantum Equivalence Principle", arXiv:1903.01289, (2019).

[151] Julian De Vuyst, Philipp A. Hoehn, and Artur Tsobanjan, "On the relation between perspective-neutral, algebraic, and effective quantum reference frames", arXiv:2507.14131, (2025).

[152] Samuel Fedida and Jan Głowacki, "Foundations of Relational Quantum Field Theory I: Scalars", arXiv:2507.21601, (2025).

[153] V. Vilasini, Lin-Qing Chen, Liuhang Ye, and Renato Renner, "Events and their Localisation are Relative to a Lab", arXiv:2505.21797, (2025).

[154] Lee Smolin, "Quantum reference frames and triality", arXiv:2007.05957, (2020).

[155] Houri Ziaeepour, "$SU(\infty)$ Quantum Gravity: Emergence of Gravity in an Infinitely Divisible Quantum Universe", arXiv:2301.02813, (2023).

[156] Henrique Gomes, Simon Langenscheidt, and Daniele Oriti, "Boundaries, frames and the issue of physical covariance", arXiv:2412.00993, (2024).

[157] Ashmeet Singh, "Quantum space, quantum time, and relativistic quantum mechanics", Quantum Studies: Mathematics and Foundations 9 1, 35 (2022).

[158] Alexander R. H. Smith, "Communicating without shared reference frames", Physical Review A 99 5, 052315 (2019).

[159] Martin Bojowald and Artur Tsobanjan, "Algebraic properties of quantum reference frames: Does time fluctuate?", arXiv:2211.04520, (2022).

[160] Rodolfo Gambini, Luis Pedro García-Pintos, and Jorge Pullin, "Single-world consistent interpretation of quantum mechanics from fundamental time and length uncertainties", Physical Review A 100 1, 012113 (2019).

[161] Luca Marchetti and Edward Wilson-Ewing, "Relational observables in group field theory", Classical and Quantum Gravity 42 15, 155008 (2025).

[162] Augustin Vanrietvelde, Octave Mestoudjian, and Pablo Arrighi, "Partitions in quantum theory", arXiv:2506.22218, (2025).

[163] Yigit Yargic, "Path Integral in Modular Space", arXiv:2002.01604, (2020).

[164] Julian Wechs and Ognyan Oreshkov, "Subsystem decompositions of quantum evolutions and transformations between causal perspectives", arXiv:2411.16504, (2024).

[165] Charalampos Theofilis and Wolfgang Wieland, "Foundational Structure of Local Amplitudes in Quantum Gravity", arXiv:2508.09679, (2025).

[166] Jianhao M. Yang, "Quantum Entanglement Induced by Gravitational Potential", arXiv:1903.04896, (2019).

[167] Christopher J. Fewster, Daan W. Janssen, and Kasia Rejzner, "Semi-local observables, edge modes and quantum reference frames in quantum electromagnetism: an algebraic approach", arXiv:2508.20939, (2025).

[168] Antoine Soulas, Guilherme Franzmann, and Andrea Di Biagio, "On the emergence of preferred structures in quantum theory", arXiv:2512.07468, (2025).

[169] Salman Sajad Wani and Saif Al-Kuwari, "Quantum Reference Frames in Quantum Circuits: Perspective Dependent Entangling Cost and Coherence Entanglement Trade Offs", arXiv:2512.12645, (2025).

[170] Carolina Sole Panella and Wolfgang Wieland, "Fermionisation of the Aharonov--Bohm Phase on the Lightfront", arXiv:2511.19756, (2025).

[171] Jianhao M. Yang, "Simultaneous Quantization and Reduction of Constrained Systems", arXiv:2509.22747, (2025).

[172] Ludovic Varrin, "At the Corner of Quantum and Gravity", arXiv:2603.21941, (2026).

[173] Elias Rothlin, Carla Ferradini, and Lin-Qing Chen, "Error Correction in Lattice Quantum Electrodynamics with Quantum Reference Frames", arXiv:2604.06149, (2026).

[174] Javier P. Lacambra, Aidan Chatwin-Davies, Masazumi Honda, and Philipp A. Hoehn, "Gauss law codes and vacuum codes from lattice gauge theories", arXiv:2604.06087, (2026).

[175] Davide Mattei and Esteban Castro-Ruiz, "Quantum limits of a space-time reference frame", arXiv:2512.11407, (2025).

[176] Alberto Spalvieri, Sébastien Christophe Garmier, and Flaminia Giacomini, "Local Operations and Field Mediated Entanglement without a Local Tensor Product Structure", arXiv:2512.19806, (2025).

[177] Kei-Ichi Kondo, "Understanding Color Confinement through Quantum Reference Frames and Relational Observables", arXiv:2606.29668, (2026).

[178] Matthew J. Lake and Marek L. Miller, "How many degrees of freedom describe a quantum N-particle state?", arXiv:2607.16988, (2026).

[179] Kang Liu, Wei Guo, and Xiao-Mei Kuang, "Soft cutoffs in the covariant phase space of dynamical reference frames", arXiv:2603.11966, (2026).

[180] Mehdi Assanioussi, Jerzy Kowalski-Glikman, Ilkka Mäkinen, and Ludovic Varrin, "On the non-commutativity of geometric observables in different Lorentz frames", Classical and Quantum Gravity 43 12, 125002 (2026).

[181] Sergio E. Aguilar-Gutierrez, Renata Ferrero, Philipp A. Hoehn, and Luca Marchetti, "Relational path integral, effective actions and quantum frame covariance in gravity", arXiv:2607.21463, (2026).

[182] Augustin Vanrietvelde, "Specifying the operational meaning of quantum reference frames", arXiv:2607.03417, (2026).

[183] Časlav Brukner, Esteban Castro-Ruiz, and Marius Krumm, "An Operational Resolution of the Third-Particle Paradox", arXiv:2607.20815, (2026).

[184] Alessandro Palumbo and Luca Apadula, "Frame-Dependent Traces and the Third-Particle Paradox", arXiv:2607.21703, (2026).

[185] Caslav Brukner, "Schroedinger's Equation at 100: The Wave Picture That Helped and Possibly Hurt", arXiv:2604.26325, (2026).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-22 02:24:16) and SAO/NASA ADS (last updated successfully 2026-08-22 02:24:18). The list may be incomplete as not all publishers provide suitable and complete citation data.

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