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arXiv:quant-ph/9603023 · Physical Review A

Collective tests for quantum nonlocality

Asher Peres

Published Oct 1, 1996• 180 citations
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Abstract

Pairs of spin-1/2 particles are prepared in a Werner state (namely, a mixture of singlet and random components). If the random component is large enough, the statistical results of spin measurements that may be performed on each pair separately can be reproduced by an algorithm involving local ``hidden'' variables. However, if several such pairs are tested simultaneously, a violation of the Clauser-Horne-Shimony-Holt inequality may occur, and no local hidden variable model is compatible with the results. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.2685

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Pairs of spin-1/2 particles are prepared in a Werner state (namely, a mixture of singlet and random components). If the random component is large enough, the statistical results of spin measurements that may be performed on each pair separately can be reproduced by an algorithm involving local ``hidden'' variables. However, if several such pairs are tested simultaneously, a violation of the Clauser-Horne-Shimony-Holt inequality may occur, and no local hidden variable model is compatible with the results. \textcopyright{} 1996 The American Physical Society.
This Master's thesis has two central subjects: the simulation of correlations generated by local measurements on entangled quantum states by local hidden-variables models and the revelation of hidden nonlocality. We present and detail the Werner's local model and the hidden nonlocality of some Werner states of dimension d≥5d\geq5d≥5, the Gisin-Degorre's local model for a Werner state of dimension d=2d=2d=2 and the local model of Hirsch et al. for mixtures of the singlet state and noise, all of them for projective measurements. Finally, we introduce the local model for POVMs of Hirsch et al. for a state constructed upon the singlet with noise, that still violates the CHSH inequality after local filters are applied, hence presenting the so-called genuine hidden nonlocality.
Quantum nonlocality is presented often as the most remarkable and inexplicable phenomenon known to modern science. It has been known already for a long time that the probabilistic models used to prove Bell and Clauser-Horn-Shimony-Holt inequalities (BI-CHSH) for spin polarization correlation experiments (SPCE) are incompatible with the experimental protocols of SPCE. In particular these models use the same common probability space, joint probability distributions and/or conditional independence to describe coincidence experiments in incompatible experimental settings. Strangely enough these results are not known or simply neglected. This is why we will once again reanalyze Bell locality assumptions and show that they have nothing to do with the notion of Einsteinian locality therefore their violation should not be called quantum nonlocality but rather quantum non-Kolmogorovness or quantum contextuality. Moreover if local variables describing the measuring instruments are correctly taken into account then BI-CHSH can no longer be proven and one can easily construct non-signaling probabilistic models able to reproduce the predictions of QT. The violation of BI-CHSH is considered usually as a proof that a quantum state is entangled. Since BI-CHSH are violated also in some experiments from outside the domain of quantum physics therefore the entanglement is not exclusively a quantum phenomenon. In order to further demystify these notions we show that one can prepare two macroscopic systems in such a way that simple realizable local experiments on these systems violate BI. In view of these arguments the further testing of BI-CHSH inequalities in search for the loopholes does not seem to be necessary.
Collective measurements on large quantum systems together with a majority voting strategy can lead to a violation of the Clauser-Horne-Shimony-Holt Bell inequality. In the presence of many entangled pairs, this violation decreases quickly with the number of pairs and vanishes for some critical pair number that is a function of the noise present in the system. Here we show that a different binning strategy can lead to a more substantial Bell violation when the noise is sufficiently small. Given the relation between the critical pair number and the source noise, we then present an experiment where the critical pair number is used to quantify the quality of a high visibility photon pair source. Our results demonstrate nonlocal correlations using collective measurements operating on clusters of more than 40 photon pairs.
In this paper we study the nonlocal properties of two-qubit Werner states parametrized by the visibility parameter $0\ensuremath{\leqslant}p\ensuremath{\leqslant}1$. A family of Bell inequalities is constructed that proves the two-qubit Werner states to be nonlocal for the parameter range $0.7056<p\ensuremath{\leqslant}1$. This is slightly wider than the range $0.7071<p\ensuremath{\leqslant}1$, corresponding to the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. This answers a question posed by Gisin in the positive, i.e., there exist Bell inequalities which are more efficient than the CHSH inequality in the sense that they are violated by a wider range of two-qubit Werner states.
We report the results of the first-time test of the local hidden variable theories (Bell-Clauser-Horne-Shimony-Holt) involving strongly interacting pairs of massive spin 1/21/21/2 hadrons from the decay of short-lived ($\ensuremath{\tau}<{10}^{\ensuremath{-}21}\mathrm{sec}$) 2He^{2}\mathrm{He}2He spin-singlet state, populated in the nuclear reaction $^{2}\mathrm{H}+^{1}\mathrm{H}\ensuremath{\rightarrow}^{2}\mathrm{He}+n$. The novel features of this experiment are (a) the use of an ``event-ready'' detector of nearly 100% efficiency to prepare an unbiased sample and (b) a focal-plane polarimeter of full $2\ensuremath{\pi}\text{ }\text{ }\mathrm{sr}$ acceptance with a random ``post selection'' of the reference axes. The spin-correlation function is deduced to be ${S}_{\mathrm{exp}}(\ensuremath{\pi}/4)=2.83\ifmmode\pm\else\textpm\fi{}{0.24}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.07}_{\mathrm{sys}}$. This result is in agreement with nonlocal quantum mechanical prediction and it violates the Bell-CHSH inequality of $|S|\ensuremath{\le}2$ at a confidence level of 99.3%.