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Emergence of the Born rule in quantum optics

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Brian R. La Cour and Morgan C. Williamson

Applied Research Laboratories, The University of Texas at Austin, P.O. Box 8029, Austin, TX 78713-8029

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Abstract

The Born rule provides a fundamental connection between theory and observation in quantum mechanics, yet its origin remains a mystery. We consider this problem within the context of quantum optics using only classical physics and the assumption of a quantum electrodynamic vacuum that is real rather than virtual. The connection to observation is made via classical intensity threshold detectors that are used as a simple, deterministic model of photon detection. By following standard experimental conventions of data analysis on discrete detection events, we show that this model is capable of reproducing several observed phenomena thought to be uniquely quantum in nature, thus providing greater elucidation of the quantum-classical boundary.

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► References

[1] J. von Neumann. Mathematische Grundlagen der Quantentheorie. Springer, 1931.

[2] J. S. Bell. On the Einstein Podolsky Rosen paradox. Physics, 1:195, 1964.

[3] W. M. de Muynck. Foundations of Quantum Mechanics, An Empiricist Approach. Kluwer Academic Publishers, 2002.

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

[5] B. Hensen et al. Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres. Nature, 526:682, 2015. https:/​/​doi.org/​10.1038/​nature15759.
https:/​/​doi.org/​10.1038/​nature15759

[6] M. Giustina et al. Significant-loophole-free test of Bell’s theorem with entangled photons. Physical Review Letters, 115:250401, 2015. https:/​/​doi.org/​10.1103/​PhysRevLett.115.250401.
https:/​/​doi.org/​10.1103/​PhysRevLett.115.250401

[7] L. K. Shalm et al. Strong loophole-free test of local realism. Physical Review Letters, 115:250402, 2015. https:/​/​doi.org/​10.1103/​PhysRevLett.115.250402.
https:/​/​doi.org/​10.1103/​PhysRevLett.115.250402

[8] W. Rosenfeld et al. Event-ready bell test using entangled atoms simultaneously closing detection and locality loopholes. Physical Review Letters, 119:010402, 2017. https:/​/​doi.org/​10.1103/​PhysRevLett.119.010402.
https:/​/​doi.org/​10.1103/​PhysRevLett.119.010402

[9] P. Bierhorst et al. Experimentally generated randomness certified by the impossibility of superluminal signals. Nature, 556:223, 2018. https:/​/​doi.org/​10.1038/​s41586-018-0019-0.
https:/​/​doi.org/​10.1038/​s41586-018-0019-0

[10] V. B. Berestetskii, L. P. Pitaevskii, and E. M. Lifshitz. Quantum Electrodynamics, volume 4. Elsevier, 2nd edition, 1982.

[11] P. W. Milonni. The Quantum Vacuum. An Introduction to Quantum Electrodynamics. Academic Press, 1994.

[12] N. P. Landsman. Compendium of Quantum Physics, chapter The Born rule and its interpretation. Springer, 2008.

[13] M. Born. Zur quantenmechanik der stoßvorgänge. Zeitschrift für Physik, 37:863, 1926. https:/​/​doi.org/​10.1007/​BF01397477.
https:/​/​doi.org/​10.1007/​BF01397477

[14] A. M. Gleason. Measures on the closed subspaces of a Hilbert space. Journal of Mathematical Mechanics, 6:885, 1957. https:/​/​doi.org/​10.1007/​978-94-010-1795-4_7.
https:/​/​doi.org/​10.1007/​978-94-010-1795-4_7

[15] D. Deutsch. Quantum theory of probability and decisions. Proceedings of the Royal Society A, 455:3129, 1999. https:/​/​doi.org/​10.1098/​rspa.1999.0443.
https:/​/​doi.org/​10.1098/​rspa.1999.0443

[16] H. Barnum, C. M. Caves, J. Finkelstein, C. A. Fuchs, and R. Schack. Quantum probability from decision theory? Proceedings of The Royal Society, A456:1175, 2000. https:/​/​doi.org/​10.1098/​rspa.2000.0557.
https:/​/​doi.org/​10.1098/​rspa.2000.0557

[17] W. H. Zurek. Probabilities from entanglement, Born’s rule $p_k = |psi_k| ^2$ from envariance. Physical Review A, 71:052105, 2005. https:/​/​doi.org/​10.1103/​PhysRevA.71.052105.
https:/​/​doi.org/​10.1103/​PhysRevA.71.052105

[18] M. Schlosshauer and A. Fine. On Zurek’s derivation of the Born rule. Foundations of Physics, 35:197, 2005. https:/​/​doi.org/​10.1007/​s10701-004-1941-6.
https:/​/​doi.org/​10.1007/​s10701-004-1941-6

[19] L. Masanes, T. D. Galley, and M. P. Müller. The measurement postulates of quantum mechanics are operationally redundant. Nature Communications, 10:1361, 2019. https:/​/​doi.org/​10.1038/​s41467-019-09348-x.
https:/​/​doi.org/​10.1038/​s41467-019-09348-x

[20] A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen. Understanding quantum measurement from the solution of dynamical models. Physics Reports, 525:1, 2013. https:/​/​doi.org/​10.1016/​j.physrep.2012.11.001.
https:/​/​doi.org/​10.1016/​j.physrep.2012.11.001

[21] L. de la Peña and A. M. Cetto. The Quantum Dice: An Introduction to Stochastic Electrodynamics. Kluwer, 1995.

[22] A. Casado, T. W. Marshall, and E. Santos. Parametric downconversion experiments in the Wigner representation. Journal of the Optical Society of America B, 14:494, 1997. https:/​/​doi.org/​10.1364/​JOSAB.14.000494.
https:/​/​doi.org/​10.1364/​JOSAB.14.000494

[23] T. W. Marshall and E. Santos. Stochastic optics: A reaffirmation of the wave nature of light. Foundations of Physics, 18:185, 1988. https:/​/​doi.org/​10.1007/​BF01882931.
https:/​/​doi.org/​10.1007/​BF01882931

[24] G. Adenier. Violation of Bell inequalities as a violation of fair sampling in threshold detectors. In AIP Conference Proceedings 1101, page 8, 2009. https:/​/​doi.org/​10.1063/​1.3109977.
https:/​/​doi.org/​10.1063/​1.3109977

[25] B. La Cour. A locally deterministic, detector-based model of quantum measurement. Foundations of Physics, 44:1059, 2014. https:/​/​doi.org/​10.1007/​s10701-014-9829-6.
https:/​/​doi.org/​10.1007/​s10701-014-9829-6

[26] A. Khrennikov. Beyond Quantum. Pan Stanford Publishing, 2014.

[27] M. Planck. Eine neue strahlungshypothese. Verhandlungen der Deutschen Physikalischen Gesellschaft, 13:138, 1911.

[28] T. W. Marshall. Random electrodynamics. Proceedings of the Royal Society, A276:475, 1963. http:/​/​doi.org/​10.1098/​rspa.1963.0220.
https:/​/​doi.org/​10.1098/​rspa.1963.0220

[29] M. Ibison and B. Haisch. Quantum and classical statistics of the electromagnetic zero-point field. Physical Review A, 54:2737, 1996. https:/​/​doi.org/​10.1103/​PhysRevA.54.2737.
https:/​/​doi.org/​10.1103/​PhysRevA.54.2737

[30] A. Lasota and M. Mackey. Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics. Springer, 2nd edition, 1998.

[31] H. M. França and T. W. Marshall. Excited states in stochastic electrodynamics. Physical Review A, 38:3258, 1988. https:/​/​doi.org/​10.1103/​PhysRevA.38.3258.
https:/​/​doi.org/​10.1103/​PhysRevA.38.3258

[32] M. Ossiander et al. Absolute timing of the photoelectric effect. Nature, 561:374, 2018. https:/​/​doi.org/​10.1038/​s41586-018-0503-6.
https:/​/​doi.org/​10.1038/​s41586-018-0503-6

[33] H. Shibata, K. Shimizu, H. Takesue, and Y. Tokura. Ultimate low system dark count rate for superconducting nanowire single-photon detector. Optics Letters, 40:3428, 2015. https:/​/​doi.org/​10.1364/​OL.40.003428.
https:/​/​doi.org/​10.1364/​OL.40.003428

[34] N. L. Johnson, S. Kotz, and N. Balakrishnan. Continuous Univariate Distributions. John Wiley and Sons, 1994.

[35] K. Cahill and R. Glauber. Density operators and quasiprobability distributions. Physical Review, 177:1882, 1969. https:/​/​doi.org/​10.1103/​PhysRev.177.1882.
https:/​/​doi.org/​10.1103/​PhysRev.177.1882

[36] K. Fujii and T. Suzuki. A new symmetric expression of Weyl ordering. Modern Physics Letters A, 19:827, 2004. https:/​/​doi.org/​10.1142/​S021773230401374X.
https:/​/​doi.org/​10.1142/​S021773230401374X

[37] B. F. Levine, D. G. Bethea, and J. C. Campbell. Near room temperature 1.3um single photon counting with a ingaas avalanche photodiode. Electronics Letters, 20:596, 1984. https:/​/​doi.org/​10.1049/​el:19840411.
https:/​/​doi.org/​10.1049/​el:19840411

[38] J. Oh, C. Anonelli, M. Tur, and M. Brodsky. Method for characterizing single photon detectors in saturation regime by cw laser. Optics Express, 18:5906, 2010. https:/​/​doi.org/​10.1364/​OE.18.005906.
https:/​/​doi.org/​10.1364/​OE.18.005906

[39] R. Loudon. Non-classical effects in the statistical properties of light. Reports on Progress in Physics, 43:913, 1980. https:/​/​doi.org/​10.1088/​0034-4885/​43/​7/​002.
https:/​/​doi.org/​10.1088/​0034-4885/​43/​7/​002

[40] R. W. Boyd, S. G. Lukishova, and V. N. Zadkov, editors. The First Single Photon Sources and Single Photon Interference Experiments, chapter 1. Springer, 2019.

[41] P. Grangier, G. Roger, and A. Aspect. Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences. Europhysics Letters, 1:173, 1986. https:/​/​doi.org/​10.1209/​0295-5075/​1/​4/​004.
https:/​/​doi.org/​10.1209/​0295-5075/​1/​4/​004

[42] J. J. Thorn et al. Observing the quantum behavior of light in an undergraduate laboratory. American Journal of Physics, 79:1210, 2004. https:/​/​doi.org/​10.1119/​1.1737397.
https:/​/​doi.org/​10.1119/​1.1737397

[43] P. Kwiat and H. Weinfurter. Embedded Bell-state analysis. Physical Review A, 58:R2623, 1998. https:/​/​doi.org/​10.1103/​PhysRevA.58.R2623.
https:/​/​doi.org/​10.1103/​PhysRevA.58.R2623

[44] V. Jacques, E. Wu, F. Grosshans, F. Treussart, P. Grangier, A. Aspect, and J.-F. Roch. Experimental realization of Wheeler’s delayed-choice gedanken experiment. Science, 315:966, 2007. https:/​/​doi.org/​10.1126/​science.1136303.
https:/​/​doi.org/​10.1126/​science.1136303

[45] F. Mezzadri. How to generate random matrices from the classical compact groups. Notices of the AMS, 54:592, 2007. http:/​/​www.ams.org/​notices/​200705/​index.html.
http:/​/​www.ams.org/​notices/​200705/​index.html

[46] D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White. Measurement of qubits. Physical Review A, 64:052312, 2001. https:/​/​doi.org/​10.1103/​PhysRevA.64.052312.
https:/​/​doi.org/​10.1103/​PhysRevA.64.052312

[47] Z. Hradil. Quantum-state estimation. Physical Review A, 55:R1561(R), 1997. https:/​/​doi.org/​10.1103/​PhysRevA.55.R1561.
https:/​/​doi.org/​10.1103/​PhysRevA.55.R1561

[48] Z. Hradil, J. Summhammer, G. Badurek, and H. Rauch. Reconstruction of the spin state. Physical Review A, 62:014101, 2000. https:/​/​doi.org/​10.1103/​PhysRevA.62.014101.
https:/​/​doi.org/​10.1103/​PhysRevA.62.014101

[49] J. B. Altepeter, D. F. V. James, and P. G. Kwiat. Lecture Notes in Physics, chapter Quantum State Estimation. Springer, Berlin, 2004.

[50] Kwiat Quantum Information Group. Guide to Quantum State Tomography. http:/​/​research.physics.illinois.edu/​QI/​Photonics/​Tomography/​ Accessed 20 December 2019.
http:/​/​research.physics.illinois.edu/​QI/​Photonics/​Tomography/​

[51] A. Peres. Separability criterion for density matrices. Physical Review Letters, 77:1413, 1996. https:/​/​doi.org/​10.1103/​PhysRevLett.77.1413.
https:/​/​doi.org/​10.1103/​PhysRevLett.77.1413

[52] P. Horodecki M. Horodecki and R. Horodecki. Separability of mixed states: necessary and sufficient conditions. Physics Letters A, 223:1, 1996. https:/​/​doi.org/​10.1016/​S0375-9601(96)00706-2.
https:/​/​doi.org/​10.1016/​S0375-9601(96)00706-2

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Source: https://quantum-journal.org/papers/q-2020-10-26-350/

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