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Physical Review Letters

Spin Correlations of Strongly Interacting Massive Fermion Pairs as a Test of Bell’s Inequality

Hideyuki SAKAI, T. Saito, T. Ikeda, K. Itoh, T. Kawabata, H. Kuboki, Yukie Maeda, Naoki Matsui, C. Rangacharyulu, M. Sasano, Y. Satou, K. Sekiguchi, Kenji Suda, A. Tamii, Tomohiro Uesaka, K. Yako

Published Oct 13, 2006• 81 citations
Publisher

Abstract

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 $1/2$ hadrons from the decay of short-lived ($\ensuremath{\tau}<{10}^{\ensuremath{-}21}\mathrm{sec}$) $^{2}\mathrm{He}$ 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%.

DOI
10.1103/physrevlett.97.150405

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Test of local realism via entangled ΛΛˉ\Lambda \bar{\Lambda }ΛΛˉ system
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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.
We show that a pair of massive relativistic spin-1/2 particles prepared in a maximally entangled spin state in general is not capable of maximally violating the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequalities without a postselection of the particles' momenta, representing a major difference in relation to nonrelativistic systems. This occurs because the quantization axis of the measurements performed on each particle depends on the particle velocity, such that it is not possible to define a reduced density matrix for the particles' spin. We also show that the amount of violation of the CHSH inequality depends on the reference frame and that in some frames the inequality may not be violated.
Arising out of the EPR debate, the Bell and Wigner inequalities of quantum theory are experimentally testable relations which address the question of quantum completeness. This thesis provides feasibility results for a fermionic test of the Bell inequality, and the first known attempt to investigate the completeness question through the Wigner relation. Such a test is made possible by the production of an entangled p-p singlet at the KVI research facility in Groningen, the Netherlands, through the reactions 12C(d,2He)12B and p(d,2He)n. The p-p spin-correlations are analyzable via the KVI's 2-pi polarimeter acceptance, which eliminates loopholes common to previous experiments. The results distinguish between a hidden variables and quantum mechanical description of the universe. Also presented is a critique of the GHZ argument against the existence of local hidden variables.