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

Augustin Vanrietvelde; Philipp A. Hoehn; Flaminia Giacomini; Esteban Castro-Ruiz

doi:10.22331/q-2020-01-27-225

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).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

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

Cited by

[1] Angel Ballesteros, Flaminia Giacomini, and Giulia Gubitosi, "The group structure of dynamical transformations between quantum reference frames", Quantum 5, 470 (2021).

[2] 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).

[3] Laurent Freidel, Marc Geiller, and Wolfgang Wieland, Handbook of Quantum Gravity 1 (2024) ISBN:978-981-19-3079-9.

[4] Philipp A Höhn and Augustin Vanrietvelde, "How to switch between relational quantum clocks", New Journal of Physics 22 12, 123048 (2020).

[5] Sylvain Carrozza and Philipp A. Höhn, "Edge modes as reference frames and boundary actions from post-selection", Journal of High Energy Physics 2022 2, 172 (2022).

[6] Luciano Gabbanelli and Silvia De Bianchi, "Cosmological implications of the hydrodynamical phase of group field theory", General Relativity and Gravitation 53 7, 66 (2021).

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

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

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

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

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

[12] 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).

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

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

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

[16] 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).

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

[18] 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).

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

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

[21] 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).

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

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

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

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

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

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

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

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

[34] 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).

[35] 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).

[36] 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).

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

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

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

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

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

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

[43] 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).

[44] 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).

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

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

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

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

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

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

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

[54] 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).

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

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

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

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

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

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

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

[62] 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).

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

[64] 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).

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

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

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

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

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

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

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

[72] 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).

[73] 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).

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

[75] 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).

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

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

[78] 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).

[79] Julian De Vuyst, Stefan Eccles, Philipp A. Hoehn, and Josh Kirklin, "Gravitational entropy is observer-dependent", arXiv:2405.00114, (2024).

[80] Eugenio Bianchi, Pietro Dona, and Rishabh Kumar, "Non-abelian symmetry-resolved entanglement entropy", arXiv:2405.00597, (2024).

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

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

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

[84] 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).

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

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

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

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

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

[90] Sylvain Carrozza, Stefan Eccles, and Philipp A. Hoehn, "Edge modes as dynamical frames: charges from post-selection in generally covariant theories", arXiv:2205.00913, (2022).

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

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

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

[94] 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).

[95] Ashmeet Singh, "Quantum Space, Quantum Time, and Relativistic Quantum Mechanics", arXiv:2004.09139, (2020).

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

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

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

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

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

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-16 02:49:16) and SAO/NASA ADS (last updated successfully 2024-05-16 02:49:17). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.