Inequalities based on local realism free of measurement-setting loophole and their violations in entangled baryons

D. Boschi, F. De Martini, Giovanni Di Giuseppe

Yu Shi, Ji-Chong Yang

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 $$\eta _c\rightarrow \varLambda {\bar{\varLambda }}$$ ηc→ΛΛ¯ and $$\chi _{c0} \rightarrow \varLambda {\bar{\varLambda }}$$ χc0→ΛΛ¯ to test our inequalities, and show that their violations are likely to be observed with the data already collected in BESIII.

Emilio Santos

Thomas Scheidl, Rupert Ursin, Johannes Kofler +8 more

Bell's theorem shows that local realistic theories place strong restrictions on observable correlations between different systems, giving rise to Bell's inequality which can be violated in experiments using entangled quantum states. Bell's theorem is based on the assumptions of realism, locality, and the freedom to choose between measurement settings. In experimental tests, "loopholes" arise which allow observed violations to still be explained by local realistic theories. Violating Bell's inequality while simultaneously closing all such loopholes is one of the most significant still open challenges in fundamental physics today. In this paper, we present an experiment that violates Bell's inequality while simultaneously closing the locality loophole and addressing the freedom-of-choice loophole, also closing the latter within a reasonable set of assumptions. We also explain that the locality and freedom-of-choice loopholes can be closed only within nondeterminism, i.e., in the context of stochastic local realism.

Giovanni Di Giuseppe, F. De Martini, D. Boschi

Alejandro Andrés Hnilo

The recent loophole-free experiments have confirmed the violation of Bell’s inequalities in nature. Yet, in order to insert measured values in Bell’s inequalities, it is unavoidable to make a hypothesis similar to “ergodicity at the hidden variables level”. This possibility opens a promising way out from the old controversy between quantum mechanics and local realism. Here, I review the reason why such a hypothesis (actually, it is one of a set of related hypotheses) in addition to local realism is necessary, and present a simple example, related to Bell’s inequalities, where the hypothesis is violated. This example shows that the violation of the additional hypothesis is necessary, but not sufficient, to violate Bell’s inequalities without violating local realism. The example also provides some clues that may reveal the violation of the additional hypothesis in an experiment.