Unexpected reemergence of the von Neumann theorem

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 79, Issue 2, 2009, Pages

  Zukowski, Marek ^a  

^a UNIVERSITY OF GDA SK   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTUM ELECTRONICS; QUANTUM OPTICS;

CLASSICAL FIELDS; EIGEN VALUES; HIDDEN VARIABLES; INDIVIDUAL SYSTEMS; OPTICAL REALIZATIONS; QUANTUM SYSTEMS;

STOCHASTIC MODELS;

EID: 62549149908     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.79.024103     Document Type: Article

References (21)

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3. J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932)
4. Mathematical Foundations of Quantum Mechanics (Princeton University, Princeton, NJ, 1955).
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6. N. D. Mermin, Rev. Mod. Phys. 65, 803 (1993). 10.1103/RevModPhys.65.803
7. G. Brida, I. Degiovanni, M. Genovese, V. Schettini, S. Polyakov, and A. Migdall, Opt. Express 16, 11750 (2008) 10.1364/OE.16.011750
8. for the latest version of such an experiment see G. Brida, I. P. Degiovanni, M. Genovese, F. Piacentini, V. Schettini, N. Gisin, S. V. Polyakov, and A. Migdall, e-print arXiv:0811.3376.
9. J. S. Bell, Physics 1, 195 (1964);
10. for a review see M. Genovese, Phys. Rep. 413, 319 (2005). 10.1016/j.physrep.2005.03.003
11. R. Gill, G. Weihs, A. Zeilinger, and M. Zukowski, Proc. Natl. Acad. Sci. U.S.A. 99, 14632 (2002) 10.1073/pnas.182536499
12. R. Gill, G. Weihs, A. Zeilinger, and M. Zukowski, Europhys. Lett. 61, 282 (2003). 10.1209/epl/i2003-00230-6
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14. R. Alicki, e-print arXiv:0810.4708.
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16. Because none of the pairs of out of these three observables commutes. In the laboratory this implies different operational situations.
17. The inequality is 0≤A (x) ≤B (x), where, in the language of this comment, x is a hidden variable. This is an assumption of a specific distinguishing property of the minimal models, which is not derivable from the properties of the observed averages.
18. Here the measurement outcomes, Xk, play the role of hidden variables.
19. In simpler words there is no distinction in the Young-type interference between classical fields and those revealing quantum nature.
20. One could argue here that one might split the incoming classical beams into two pairs and send them into two differently tuned Mach-Zehnder interferometers and then observe fluctuations giving negative values, but such an experiment does not model the two output situation assumed in the example of.
21. The statistics of PDC radiation enables the heralding employed in the experiment: upon registration of an idler photon one can expect just one click (single photon) at just one of the detectors in the observation station behind the polarization analyzers. This feature is missing in the classical model presented here. For the experiment one could use other sources of single photons, such as quantum dots, color centers in diamonds, etc. In such a case the single photon, antibunched, nature of emissions is warranted by the workings of the source.