Events in quantum mechanics are maximally non-absolute

Source Node: 1639605

George Moreno1,2, Ranieri Nery1, Cristhiano Duarte1,3, and Rafael Chaves1,4

1International Institute of Physics, Federal University of Rio Grande do Norte, 59078-970, Natal, Brazil
2Departamento de Computação, Universidade Federal Rural de Pernambuco, 52171-900, Recife, Pernambuco, Brazil
3School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
4School of Science and Technology, Federal University of Rio Grande do Norte, Natal, Brazil

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Abstract

The notorious quantum measurement problem brings out the difficulty to reconcile two quantum postulates: the unitary evolution of closed quantum systems and the wave-function collapse after a measurement. This problematics is particularly highlighted in the Wigner’s friend thought experiment, where the mismatch between unitary evolution and measurement collapse leads to conflicting quantum descriptions for different observers. A recent no-go theorem has established that the (quantum) statistics arising from an extended Wigner’s friend scenario is incompatible when one try to hold together three innocuous assumptions, namely no-superdeterminism, parameter independence and absoluteness of observed events. Building on this extended scenario, we introduce two novel measures of non-absoluteness of events. The first is based on the EPR2 decomposition, and the second involves the relaxation of the absoluteness hypothesis assumed in the aforementioned no-go theorem. To prove that quantum correlations can be maximally non-absolute according to both quantifiers, we show that chained Bell inequalities (and relaxations thereof) are also valid constraints for Wigner’s experiment.

The measurement problem emerges from the incompatibility between two of the quantum postulates. On the one hand, we have the Schrödinger equation, which tells us that the evolution of the wave function is governed by a smooth and reversible unitary transformation. On the other side, we have the measurement postulate, telling us what is the probability of a certain result when a measurement is performed, implying the so-called collapse of the wavefunction, a non-unitary, abrupt and irreversible transformation.
To illustrate the problem, the Hungarian-American physicist Eugene Wigner proposed in 1961 an imaginary experiment, now called Wigner’s friend experiment. Charlie, an isolated observer in his laboratory, performs a measurement on a quantum system in a superposition of two states. He randomly obtains one of two possible measurement results. In contrast, Alice acts as a superobserver, and describes her friend Charlie, the laboratory and the system being measured as a large composite quantum system. So, from Alice’s perspective, her friend Charlie exists in a coherent superposition, entangled with the result of his measurement. That is, from Alice’s point of view, the quantum state does not associate a well-defined value with the result of Charlie’s measurement. Thus, these two descriptions, that of Alice or that of her friend Charlie, lead to different results, which in principle could be compared experimentally. It might seem a little strange, but here lies the problem: quantum mechanics doesn’t tell us where to draw the line between the classical and quantum worlds. In principle, the Schrödinger equation applies to atoms and electrons as well as to macroscopic objects such as cats and human friends. Nothing in the theory tells us what is to be analyzed through unitary evolutions or the formalism of measurement operators.
If we now imagine two superobservers, described by Alice and Bob, each of them measuring their own laboratory containing their respective friends, Charlie and Debbie and the systems they measure, the statistics obtained by Alice and Bob should be classical, that is, should not be able to violate any Bell inequality. After all, by the measurement postulate, all non-classicality of the system should have been extinguished when Charlie and Debbie performed their measurements. Mathematically, we can describe this situation by a set of hypotheses. The first hypothesis is the absoluteness of events (AoE). As in a Bell experiment, what we have experimental access to is probability distribution p(a,b|x,y), the measurement results of Alice and Bob, given that they measured a certain observable. But if measurements made by observers really are absolute events, then this observable probability should come from a joint probability in which Charlie and Debbie’s measurement results can also be defined. When combined with the assumptions of measurement independence and no-signalling, AoE leads to experimentally testable constraints, Bell inequalities that are violated by quantum correlations, thus proving the incompatibility of quantum theory with the conjunction of such assumptions.
In this paper, we show that we can relax the AoE assumption and still obtain quantum violations of the corresponding Bell inequalities. By considering two different and complementary manners to quantify the relaxation of AoE, we quantify how much the predictions from an observer and a superobserver should disagree in order to reproduce the quantum predictions for such an experiment. In fact, as we prove, to reproduce the possible correlations allowed by quantum mechanics, this deviation has to be maximum, corresponding to the case where the measurement results of Alice and Charlie or Bob and Debbie are completely uncorrelated. In other terms, quantum theory allows for maximally non-absolute events.

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â–º References

[1] E. P. Wigner, The problem of measurement, American Journal of Physics 31, 6 (1963).
https:/​/​doi.org/​10.1119/​1.1969254

[2] M. Schlosshauer, Decoherence, the measurement problem, and interpretations of quantum mechanics, Reviews of Modern physics 76, 1267 (2005).
https:/​/​doi.org/​10.1103/​RevModPhys.76.1267

[3] M. F. Pusey, An inconsistent friend, Nature Physics 14, 977–978 (2018).
https:/​/​doi.org/​10.1038/​s41567-018-0293-7

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

[5] H. Everett, “Relative state” formulation of quantum mechanics, The Many Worlds Interpretation of Quantum Mechanics , 141 (2015).
https:/​/​doi.org/​10.1515/​9781400868056-003

[6] D. Bohm and J. Bub, A proposed solution of the measurement problem in quantum mechanics by a hidden variable theory, Reviews of Modern Physics 38, 453 (1966).
https:/​/​doi.org/​10.1103/​RevModPhys.38.453

[7] S. Hossenfelder and T. Palmer, Rethinking superdeterminism, Frontiers in Physics 8, 139 (2020).
https:/​/​doi.org/​10.3389/​fphy.2020.00139

[8] G. Hooft, The free-will postulate in quantum mechanics, arXiv preprint quant-ph/​0701097 (2007).
https:/​/​doi.org/​10.48550/​arXiv.quant-ph/​0701097
arXiv:quant-ph/0701097

[9] H. Price, Toy models for retrocausality, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39, 752 (2008).
https:/​/​doi.org/​10.1016/​j.shpsb.2008.05.006

[10] H. P. Stapp, The copenhagen interpretation, American journal of physics 40, 1098 (1972).
https:/​/​doi.org/​10.1119/​1.1986768

[11] C. Rovelli, Relational quantum mechanics, International Journal of Theoretical Physics 35, 1637 (1996).
https:/​/​doi.org/​10.1007/​BF02302261

[12] C. M. Caves, C. A. Fuchs, and R. Schack, Quantum probabilities as bayesian probabilities, Physical review A 65, 022305 (2002).
https:/​/​doi.org/​10.1103/​PhysRevA.65.022305

[13] A. Bassi and G. Ghirardi, Dynamical reduction models, Physics Reports 379, 257 (2003).
https:/​/​doi.org/​10.1016/​S0370-1573(03)00103-0

[14] G. C. Ghirardi, A. Rimini, and T. Weber, Unified dynamics for microscopic and macroscopic systems, Physical review D 34, 470 (1986).
https:/​/​doi.org/​10.1103/​PhysRevD.34.470

[15] R. Penrose, On gravity’s role in quantum state reduction, General relativity and gravitation 28, 581 (1996).
https:/​/​doi.org/​10.1007/​BF02105068

[16] C. Brukner, On the quantum measurement problem (2015), arXiv:1507.05255 [quant-ph].
https:/​/​doi.org/​10.48550/​arXiv.1507.05255
arXiv:1507.05255

[17] Č. Brukner, A no-go theorem for observer-independent facts, Entropy 20, 350 (2018).
https:/​/​doi.org/​10.3390/​e20050350

[18] E. G. Cavalcanti and H. M. Wiseman, Implications of local friendliness violation for quantum causality, Entropy 23, 10.3390/​e23080925 (2021).
https:/​/​doi.org/​10.3390/​e23080925

[19] D. Frauchiger and R. Renner, Quantum theory cannot consistently describe the use of itself, Nature communications 9, 1 (2018).
https:/​/​doi.org/​10.1038/​s41467-018-05739-8

[20] P. A. Guérin, V. Baumann, F. Del Santo, and ÄŒ. Brukner, A no-go theorem for the persistent reality of Wigner’s friends perception, Communications Physics 4, 1 (2021).
https:/​/​doi.org/​10.1038/​s42005-021-00589-1

[21] R. Healey, Quantum theory and the limits of objectivity, Foundations of Physics 48, 1568 (2018).
https:/​/​doi.org/​10.1007/​s10701-018-0216-6

[22] M. Proietti, A. Pickston, F. Graffitti, P. Barrow, D. Kundys, C. Branciard, M. Ringbauer, and A. Fedrizzi, Experimental test of local observer independence, Science advances 5, eaaw9832 (2019).
https:/​/​doi.org/​10.1126/​sciadv.aaw9832

[23] M. Å»ukowski and M. Markiewicz, Physics and metaphysics of Wigner’s friends: Even performed premeasurements have no results, Physical Review Letters 126, 130402 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.126.130402

[24] E. G. Cavalcanti, The view from a Wigner bubble, Foundations of Physics 51, 1 (2021).
https:/​/​doi.org/​10.1007/​s10701-021-00417-0

[25] K.-W. Bong, A. Utreras-Alarcón, F. Ghafari, Y.-C. Liang, N. Tischler, E. G. Cavalcanti, G. J. Pryde, and H. M. Wiseman, A strong no-go theorem on the Wigner’s friend paradox, Nature Physics 16, 1199 (2020).
https:/​/​doi.org/​10.1038/​s41567-020-0990-x

[26] Z.-P. Xu, J. Steinberg, H. C. Nguyen, and O. Gühne, No-go theorem based on incomplete information of Wigner about his friend (2021), arXiv:2111.15010 [quant-ph].
https:/​/​doi.org/​10.48550/​arXiv.2111.15010
arXiv:2111.15010

[27] Nuriya Nurgalieva and Lídia del Rio, Inadequacy of Modal Logic in Quantum Settings (2018), arXiv:1804.01106 [quant-ph].
https:/​/​doi.org/​10.4204/​EPTCS.287.16
arXiv:1804.01106

[28] 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, 594 (2021).
https:/​/​doi.org/​10.22331/​q-2021-08-16-524

[29] J. S. Bell, On the einstein podolsky rosen paradox, Physics Physique Fizika 1, 195 (1964).
https:/​/​doi.org/​10.1103/​PhysicsPhysiqueFizika.1.195

[30] A. C. Elitzur, S. Popescu, and D. Rohrlich, Quantum nonlocality for each pair in an ensemble, Physics Letters A 162, 25 (1992).
https:/​/​doi.org/​10.1016/​0375-9601(92)90952-I

[31] S. L. Braunstein and C. M. Caves, Wringing out better bell inequalities, Annals of Physics 202, 22 (1990).
https:/​/​doi.org/​10.1016/​0003-4916(90)90339-P

[32] A. Fine, Hidden variables, joint probability, and the bell inequalities, Physical Review Letters 48, 291 (1982).
https:/​/​doi.org/​10.1103/​PhysRevLett.48.291

[33] M. J. Hall, Local deterministic model of singlet state correlations based on relaxing measurement independence, Physical review letters 105, 250404 (2010a).
https:/​/​doi.org/​10.1103/​PhysRevLett.105.250404

[34] R. Chaves, R. Kueng, J. B. Brask, and D. Gross, Unifying framework for relaxations of the causal assumptions in bell’s theorem, Phys. Rev. Lett. 114, 140403 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.114.140403

[35] M. J. Hall and C. Branciard, Measurement-dependence cost for bell nonlocality: Causal versus retrocausal models, Physical Review A 102, 052228 (2020).
https:/​/​doi.org/​10.1103/​PhysRevA.102.052228

[36] R. Chaves, G. Moreno, E. Polino, D. Poderini, I. Agresti, A. Suprano, M. R. Barros, G. Carvacho, E. Wolfe, A. Canabarro, R. W. Spekkens, and F. Sciarrino, Causal networks and freedom of choice in bell’s theorem, PRX Quantum 2, 040323 (2021).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.040323

[37] S. Popescu and D. Rohrlich, Quantum nonlocality as an axiom, Foundations of Physics 24, 379 (1994).
https:/​/​doi.org/​10.1007/​BF02058098

[38] M. Fitzi, E. Hänggi, V. Scarani, and S. Wolf, The non-locality of n noisy popescu–rohrlich boxes, Journal of Physics A: Mathematical and Theoretical 43, 465305 (2010).
https:/​/​doi.org/​10.1088/​1751-8113/​43/​46/​465305

[39] N. D. Mermin, Extreme quantum entanglement in a superposition of macroscopically distinct states, Phys. Rev. Lett. 65, 1838 (1990).
https:/​/​doi.org/​10.1103/​PhysRevLett.65.1838

[40] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Bell nonlocality, Reviews of Modern Physics 86, 419–478 (2014).
https:/​/​doi.org/​10.1103/​RevModPhys.86.419

[41] M. J. W. Hall, Complementary contributions of indeterminism and signaling to quantum correlations, Phys. Rev. A 82, 062117 (2010b).
https:/​/​doi.org/​10.1103/​PhysRevA.82.062117

[42] S. Wehner, Tsirelson bounds for generalized clauser-horne-shimony-holt inequalities, Phys. Rev. A 73, 022110 (2006).
https:/​/​doi.org/​10.1103/​PhysRevA.73.022110

[43] A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete?, Physical review 47, 777 (1935).
https:/​/​doi.org/​10.1103/​PhysRev.47.777

[44] J. I. De Vicente, On nonlocality as a resource theory and nonlocality measures, Journal of Physics A: Mathematical and Theoretical 47, 424017 (2014).
https:/​/​doi.org/​10.1088/​1751-8113/​47/​42/​424017

[45] S. G. A. Brito, B. Amaral, and R. Chaves, Quantifying bell nonlocality with the trace distance, Phys. Rev. A 97, 022111 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.97.022111

[46] E. Wolfe, D. Schmid, A. B. Sainz, R. Kunjwal, and R. W. Spekkens, Quantifying bell: The resource theory of nonclassicality of common-cause boxes, Quantum 4, 280 (2020).
https:/​/​doi.org/​10.22331/​q-2020-06-08-280

[47] J. B. Brask and R. Chaves, Bell scenarios with communication, Journal of Physics A: Mathematical and Theoretical 50, 094001 (2017).
https:/​/​doi.org/​10.1088/​1751-8121/​aa5840

[48] I. Šupić, R. Augusiak, A. Salavrakos and A. Acín, Self-testing protocols based on the chained Bell inequalities, New Journal of Physics 18, 035013 (2016).
https:/​/​doi.org/​10.1088/​1367-2630/​18/​3/​035013

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