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Title: Loophole-free Bell's experiments and two-photon all-versus-nothing violations of local realism

Abstract

We introduce an extended version of a previous all-versus-nothing proof of impossibility of Einstein-Podolsky-Rosen's local elements of reality for two photons entangled both in polarization and path degrees of freedom (A. Cabello, quant-ph/0507259), which leads to a Bell's inequality where the classical bound is 8 and the quantum prediction is 16. A simple estimation of the detection efficiency required to close the detection loophole using this extended version gives {eta}>0.69. This efficiency is lower than that required for previous proposals.

Authors:
 [1]
  1. Departamento de Fisica Aplicada II, Universidad de Sevilla, 41012 Sevilla (Spain)
Publication Date:
OSTI Identifier:
20786414
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.050101; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; BELL THEOREM; DEGREES OF FREEDOM; EFFICIENCY; PHOTONS; POLARIZATION; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS

Citation Formats

Cabello, Adan. Loophole-free Bell's experiments and two-photon all-versus-nothing violations of local realism. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Cabello, Adan. Loophole-free Bell's experiments and two-photon all-versus-nothing violations of local realism. United States. doi:10.1103/PHYSREVA.72.0.
Cabello, Adan. Tue . "Loophole-free Bell's experiments and two-photon all-versus-nothing violations of local realism". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786414,
title = {Loophole-free Bell's experiments and two-photon all-versus-nothing violations of local realism},
author = {Cabello, Adan},
abstractNote = {We introduce an extended version of a previous all-versus-nothing proof of impossibility of Einstein-Podolsky-Rosen's local elements of reality for two photons entangled both in polarization and path degrees of freedom (A. Cabello, quant-ph/0507259), which leads to a Bell's inequality where the classical bound is 8 and the quantum prediction is 16. A simple estimation of the detection efficiency required to close the detection loophole using this extended version gives {eta}>0.69. This efficiency is lower than that required for previous proposals.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 5,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
  • We introduce two two-player quantum pseudotelepathy games based on two recently proposed all-versus-nothing (AVN) proofs of Bell's theorem [A. Cabello, Phys. Rev. Lett. 95, 210401 (2005); Phys. Rev. A 72, 050101(R) (2005)]. These games prove that Broadbent and Methot's claim that these AVN proofs do not rule out local-hidden-variable theories in which it is possible to exchange unlimited information inside the same light cone (quant-ph/0511047) is incorrect.
  • A recent proof of Bell{close_quote}s theorem without inequalities [A. Cabello, Phys.Rev.Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger{endash}type proof involving just two observers. On one hand, this new approach allows us to derive an experimentally testable Bell inequality which is violated by quantum mechanics. On the other hand, it leads to a new state-independent proof of the Kochen-Specker theorem and provides a wider perspective on the relations between the major proofs of no hidden variables.
  • A recent proof of Bell's theorem without inequalities [A. Cabello, Phys.Rev.Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger--type proof involving just two observers. On one hand, this new approach allows us to derive an experimentally testable Bell inequality which is violated by quantum mechanics. On the other hand, it leads to a new state-independent proof of the Kochen-Specker theorem and provides a wider perspective on the relations between the major proofs of no hidden variables.
  • Because of the fundamental importance of Bell's theorem, a loophole-free demonstration of a violation of local realism (LR) is highly desirable. Here, we study violations of LR involving photon pairs. We quantify the experimental evidence against LR by using measures of statistical strength related to the Kullback-Leibler (KL) divergence, as suggested by van Dam et al.[W. van Dam, R. D. Gill, and P. D. Grunwald, IEEE Trans. Inf. Theory. 51, 2812 (2005)]. Specifically, we analyze a test of LR with entangled states created from two independent polarized photons passing through a polarizing beam splitter. We numerically study the detection efficiencymore » required to achieve a specified statistical strength for the rejection of LR depending on whether photon counters or detectors are used. Based on our results, we find that a test of LR free of the detection loophole requires photon counters with efficiencies of at least 89.71%, or photon detectors with efficiencies of at least 91.11%. For comparison, we also perform this analysis with ideal unbalanced Bell states, which are known to allow rejection of LR with detector efficiencies above 2/3.« less
  • Several systems are exhibited in which the establishment of local realism violation is achieved even when some of the detectors employed are insensitive. The insensitive detectors are homodyne detectors whose task is to determine if the amplitude of a coherent state is {alpha} or {minus}{alpha} . This determination can be achieved with low quantum efficiency detectors when {vert_bar}{alpha}{vert_bar} is large. The other detectors employed determine whether there is an even number or an odd number of photons in a state. These detectors are sensitive since they are required to resolve the difference of one photon. For the examples given, themore » local realism violation is not diminished as {vert_bar}{alpha}{vert_bar} is increased. {copyright} {ital 1997} {ital The American Physical Society}« less