Abstract
Last year, the first experimental tests closing the detection loophole (also referred to as the fair sampling loophole) were performed by two experimental groups, one in Vienna and the other one in Urbana-Champaign. To violate the Bell-type inequalities (the Eberhard inequality in the first test and the Clauser–Horne inequality in the second test), one has to optimize a number of parameters involved in the experiment (angles of polarization beam splitters and quantum state parameters). We study this problem for the Eberhard inequality in detail, using the advanced method of numerical optimization, namely, the Nelder–Mead method.
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J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press (1987).
M. Giustina, Al. Mech, S. Ramelow, et al., Nature, 497, 227 (2013).
B. G. Christensen, K. T. McCusker, J. Altepeter, et al., Phys. Rev. Lett., 111, 1304 (2013).
J. Kofler, S. Ramelow, M. Giustina, and A. Zeilinger, “On Bell violation using entangled photons without the fair-sampling assumption,” arXiv: 1307.6475 [quant-ph].
J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett., 23, 880 (1969).
J. F. Clauser and M. A. Horne, Phys. Rev. D, 10, 526 (1974).
J. F. Clauser and A. Shimony, Rep. Prog. Phys., 41, 1881 (1978).
A. Shimony, “Bell’s theorem,” in: E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy, Stanford (2012); http://plato.stanford.edu/archives/win2012/entries/bell-theorem.
Ph. H. Eberhard, Phys. Rev. A, 477, 750 (1993).
N. D. Mermin, “The EPR experiment – thoughts about the ‘loophole,’ ” in: D. M. Greenberger (Ed.), Techniques and Ideas in Quantum Measurement Theory, New York Academy of Science, New York (2006), p. 422.
A. Aspect, J. Dalibard, and G. Roger, Phys. Rev. Lett., 49, 1804 (1982).
A. Aspect, Three experimental tests of Bell inequalities by the measurement of polarization correlations between photons, Ph. D Thesis, Orsay, France (1983).
A. Aspect, “Bell’s theorem: The naive view of an experimentalist,” arXiv:quant-ph/0402001.
G. Jaeger, Entanglement, Information, and the Interpretation of Quantum Mechanics (The Frontiers Collection), Springer, Heidelberg-Berlin-New York (2009).
G. Jaeger, A. Khrennikov, M. Schlosshauer, and G. Weihs (Eds.), Advances in Quantum Theory, AIP Conf. Proc., 1327 (2011).
A. Khrennikov (Ed.), Quantum Theory: Reconsideration of Foundations-5, AIP Conf. Proc., 1232 (2010).
L. Accardi, G. Adenier, C. A. Fuchs, et al. (Eds.), Foundations of Probability and Physics-5, AIP Conf. Proc., 1101 (2009).
G. Adenier, A. Yu. Khrennikov, P. Lahti, et al. (Eds.), Quantum Theory: Reconsideration of Foundations-4, AIP Conf. Proc., 962 (2008).
G. Adenier, C. Fuchs, and A. Khrennikov (Eds.), Foundations of Probability and Physics-4, AIP Conf. Proc., 889 (2007).
A. Khrennikov, Contextual Approach to Quantum Formalism, Springer, Berlin-Heidelberg-New York (2009).
S. Ramelow, “Quantum theory: Advances and problems,” Talk at A. Marcus Wallenberg Symposium “Quantum Theory: Advances and Problems” (Växjö, Sweden, 10–13 June, 2013).
J.-A. Larsson, M. Giustina, J. Kofler, et al., “Bell violation with entangled photons, free of the coincidence-time loophole,” arXiv.org/abs/1309.0712.
D. Schmid, T.-Y. Huang, R. Dirks, et al., “Polarization-dependent focusing,” Talk at the Workshop “Quantum Information and Measurement” (Rochester, New York, 17–20 June 2013).
S. V. Polyakov, E. B. Flagg, T. Thomay, and G. S. Solomon, AIP Conf. Proc., 1508, 67 (2012).
G. Weihs, T. Jennewein, C. Simon, et al., Phys. Rev. Lett., 81, 5039 (1998).
R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, et al., Nature Phys., 3, 481 (2007).
S. Lloyd, M. S. Shahriar, J. H. Shapiro, and P. R. Hemmer, Phys. Rev. Lett., 87, 167903 (2001).
O. Landry, J. A. W. van Houwelingen, A. Beveratos, et al., J. Opt. Soc. Am. B, 24,398 (2007).
H. Hübel, M. R. Vanner, T. Lederer, et al., Opt. Exp., 15, 7853 (2007).
Q. Zhang, H. Takesue, S. W. Nam, et al., Opt. Exp., 16, 5776 (2008).
I. Marcikic, H. de Riedmatten, W. Tittel, et al., Phys. Rev. Lett., 93, 180502 (2004).
H. Takesue, Opt. Exp., 14, 3453 (2006).
T. Honjo, H. Takesue, H. Kamada, et al., Opt. Exp., 15, 13957 (2007).
A. Yu. Khrennikov and I. V. Volovich, “Local realism, contextualism and loopholes in Bell’s experiments,” in: A. Yu. Khrennikov (Ed.), Foundations of Probability and Physics-2, Ser. Math. Model., Växjö University Press, Växjö, Sweden (2002), Vol. 5, p. 325.
T. Ishiwatari, A. Khrennikov, B. Nilsson, and I. Volovich, “Quantum field theory and distance effects for polarization correlations in waveguides,” in: The third Conference on Mathematical Modeling of Wave Phenomena/20th Nordic Conference on Radio Science and Communications, AIP Conf. Proc., 1106, 276 (2009).
A. Khrennikov, B. Nilsson, S. Nordebo, and I. Volovich, “Distance dependence of entangled photons in waveguides,” in: Conference FPP6 – Foundations of Probability and Physics-6, AIP Conf. Proc., 1424, 262 (2012).
A. Khrennikov, B. Nilsson, S. Nordebo, and I. Volovich. Phys. Scr., 85, 06505 (2012).
A. Khrennikov, B. Nilsson, S. Nordebo, and I. Volovich, “On the quantization of the electromagnetic field of a layered dielectric waveguide,” in: Conference QTRF6 – Quantim Theory: Reconsideration of Foundations–6, AIP Conf. Proc., 1508, 285 (2012).
J. A. Nelder and R. Mead, Comput. J., 7, 313 (1965).
D. J. Schroeder, Astronomical Optics, 2nd ed., Academic Press (1999).
J. T. Bushberg, J. A. Seibert, E. M. Leidholdt, and J. M. Boone, The Essential Physics of Medical Imaging, 2nd ed., Lippincott Williams and Wilkins, Philadelphia (2006).
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†Dedicated to the 50th anniversary of Bell’s theorem.
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Titova, P., Khrennikov, A. Modeling Tests Based on the Eberhard Inequality† . J Russ Laser Res 36, 2–16 (2015). https://doi.org/10.1007/s10946-015-9471-6
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DOI: https://doi.org/10.1007/s10946-015-9471-6