Entangled baryons: violation of inequalities based on local realism assuming dependence of decays on hidden variables
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Regular Article - Experimental Physics
Entangled baryons: violation of inequalities based on local realism assuming dependence of decays on hidden variables Yu Shi2,a , Ji-Chong Yang1,b 1 2
Department of Physics, Liaoning Normal University, Dalian 116029, China Department of Physics, Fudan University, Shanghai 200433, China
Received: 18 December 2019 / Accepted: 25 January 2020 / Published online: 11 February 2020 © The Author(s) 2020
Abstract Bell inequalities are consequences of local realism while violated by quantum mechanics. In particle physics, entangled high energy particles can be produced from a common source, and the decay of each particle plays the role of measurement. However, in a hidden variable theory, the decay could be determined by hidden variables. This loophole killed such approaches to Bell test in particle physics. It is a special form of measurement-setting or free-will loophole, which also exists in other systems. Using entangled baryons, we present new inequalities of local realism with the explicit assumption of the dependence of the decays on hidden variables, as well as the consideration of the statistical mixture of polarizations and the separation of local hidden variables for objects with spacelike distances. These violations closes the measurement-setting loophole once and for all. We propose to use the processes ηc → ΛΛ¯ and χc0 → ΛΛ¯ to test our inequalities, and show that their violations are likely to be observed with the data already collected in BESIII.
1 Introduction Entanglement in particle physics was noticed long ago [1–3], and has since been studied theoretically and experimentally [4–16]. The entangled pseudoscalar mesons are very useful in studying violations of the discrete symmetries [17–34], especially the time reversal symmetry [35–43]. Moreover, many endeavours have been made to test Bell’s inequalities (BI) [44,45] using entangled mesons [46–55] and baryons [56– 61]. For these entangled high energy particles, mostly the quantum mechanical measurement of each particle is effectively achieved through its decay, which is not a free choice of the experimentalist. Therefore, in a realistic or hidden varia e-mail:
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able theory, the decay could depend on hidden variables at the creation of the entangled pairs, leading to the violation of BI. In the derivation of BI, however, it is assumed that the decay does not depend on hidden variables. Therefore, BI implemented in terms of decays of these entangled high energy particles cannot serve to distinguish local realistic theories from quantum mechanics. Previously it has been noted that an experiment using decay time as the effective measurement basis cannot serve as as a genuine test of BI [62–64]. We emphasize that in a realistic theory, any kind of effective measurement accomplished through the decay could be determined by the hidden variables. This is actually a special form of the so-called measurement-setting for free-will loophole, well known in other syste
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