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arXiv:hep-ph/0608077 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Feasibility of testing local hidden variable theories in a Charm factory

Junli Li, Cong‐Feng Qiao

Published Oct 13, 2006• 13 citations
arXivHTMLPDF

Abstract

It is commonly believed that the local hidden variable theories (LHVTs) can be tested through measuring the Bell inequalities. This scheme, for the massive particle system, was originally set up for the entangled ${K}^{0}{\overline{K}}^{0}$ pair system from the $\ensuremath{\phi}$ factory. In this paper we show that the $J/\ensuremath{\Psi}\ensuremath{\rightarrow}{K}^{0}{\overline{K}}^{0}$ process is even more realistic for this goal. We analyze the unique properties of $J/\ensuremath{\Psi}$ in the detection of basic quantum effects, and find that it is possible to use $J/\ensuremath{\Psi}$ decay as a test of LHVTs in the future $\ensuremath{\tau}$-charm factory. Our analyses and conclusions are generally also true for other heavy onium decays.

DOI
10.1103/physrevd.74.076003

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It is commonly believed that the local hidden variable theories (LHVTs) can be tested through measuring the Bell inequalities. This scheme, for the massive particle system, was originally set up for the entangled K0K‾0{K}^{0}{\overline{K}}^{0}K0K0 pair system from the \ensuremathϕ\ensuremath{\phi}\ensuremathϕ factory. In this paper we show that the J/\ensuremathΨ\ensuremath→K0K‾0J/\ensuremath{\Psi}\ensuremath{\rightarrow}{K}^{0}{\overline{K}}^{0}J/\ensuremathΨ\ensuremath→K0K0 process is even more realistic for this goal. We analyze the unique properties of J/\ensuremathΨJ/\ensuremath{\Psi}J/\ensuremathΨ in the detection of basic quantum effects, and find that it is possible to use J/\ensuremathΨJ/\ensuremath{\Psi}J/\ensuremathΨ decay as a test of LHVTs in the future \ensuremathτ\ensuremath{\tau}\ensuremathτ-charm factory. Our analyses and conclusions are generally also true for other heavy onium decays.
Test of local realism via entangled ΛΛˉ\Lambda \bar{\Lambda }ΛΛˉ system
Abstract The non-locality of quantum correlations is a fundamental feature of quantum theory. The Bell inequality serves as a benchmark for distinguishing between predictions made by quantum theory and local hidden variable theory (LHVT). Recent advancements in photon-entanglement experiments have addressed potential loopholes and have observed significant violations of variants of Bell inequality. However, these violations do not completely disprove LHVT. To further rule out LHVT, experiments involving massive-entangled particles are necessary, in addition to those conducted with massless photons, which interact electromagnetically. In this study, we utilize (10.087±0.044)×109 J/ψ events collected with the BESIII detector at the BEPCII collider. We present the non-local correlation test of spin entanglement using a massive ΛΛbar bipartite system, which is formed and decays through strong and weak interactions, respectively. Through measurements of the angular distribution of p pbar in J/ψ→ γηc and subsequent ηc→Λ(pπ-)Λbar(pbar π+) cascade decays, a significant violation of LHVT predictions is observed in a loophole-free test of a variant of the Bell inequality, which is given by the Clauser-Horne inequality. The exclusion of LHVT is determined to be significant at a level of 5.2σ.
We review in this paper the research status on testing the completeness of Quantum mechanics in High Energy Physics, especially on the Bell Inequalities. We briefly introduce the basic idea of Einstein, Podolsky, and Rosen paradox and the results obtained in photon experiments. In the tests of Bell inequalities in high energy physics, the early attempts of using spin correlations in particle decays and later on the mixing of neutral mesons used to form the quasi-spin entangled states are covered. The related experimental results in K^0 and B^0 systems are presented and discussed. We introduce the new scheme, which is based on the non-maximally entangled state and proposed to implement in ϕfactory, in testing the Local Hidden Variable Theory. And, we also discuss the possibility in generalizing it to the tau charm factory.
A bstract Recently there has been an increased interest in possible tests of locality via Bell’s inequalities, as well as separately tests of entanglement at colliders, in particular at the LHC. These have involved various physical processes, such as tt‾ t\overline{t} tt t t ¯ , or τ + τ − production, or the decay of a Higgs boson to two vector bosons H → VV ∗ . We argue that none of these proposals constitute a test of locality via Bell’s inequality or promise unconditional observational evidence of entanglement. In all cases what is measured are the momenta of the final state particles. Using the construction proposed by Kasday (1971) in a different context, and adapted to collider scenarios by Abel, Dittmar, and Dreiner (1992), it is straightforward to construct a local hidden variable theory (LHVT) which exactly reproduces the data. This construction is only possible as the final state momenta all commute. We show that this LHVT satisfies Bell’s inequality or the related CHSH inequality as appropriate for all the proposed LHC collider tests in the literature. Thus a test of locality via Bell’s inequality is not possible at colliders. The LHVT is also by construction local, i.e. all correlations are separable. Thus an unconditional proof of entanglement is also inherently not possible at colliders. It can only be shown that the entanglement within the Standard Model consistently describes the data.
In this talk we discuss the predictions of local realistic theories for the evolution of a K0-K0bar quantum entangled pair created in the decay of the phi-meson. It is shown, in agreement with Bell's theorem, that the most general local hidden-variable model fails in reproducing the whole set of quantum-mechanical observables. We achieve this conclusion by employing two different approaches. In the first approach, the local realistic observables are deduced from the most general premises concerning locality and realism, and Bell-like inequalities are not employed. The other approach makes use of Bell's inequalities. Under particular conditions for the detection times, within the first approach the discrepancy between quantum mechanics and local realism for the asymmetry parameter turns out to be not less than 20%. A similar incompatibility can be made evident by means of a Bell-type test, by employing a Clauser-Horne-Shimony-Holt's inequality written in terms of properly normalized observables. Because of its relatively low experimental accuracy, the data obtained by the CPLEAR collaboration do not yet allow a decisive test of local realism. Such a test, both with and without the use of Bell's inequalities, should be feasible in the future at the Frascati Phi-factory.
Quantum non-locality tests have been of interest since the original EPR paper. The present paper discusses whether the CGLMP (Bell) inequalities obtained by Collins et al are possible tests for showing that quantum theory is not underpinned by local hidden variable theory (LHVT). It is found by applying Fine's theorem that the CGLMP approach involves a LHVT for the probabilities associated with measurements on two observables (each from one of the two sub-subsystems), even though the underlying probabilities for measurements of all four observables involve a hidden variable theory which is not required to be local. Although the CGLMP inequalities involve probabilities for measurements of one observable per sub-system and are compatible with the Heisenberg uncertainty principle, there is no unambiguous quantum measurement process linked to the probabilities in the CGLMP inequalities. Quantum measurements corresponding to the different classical measurements that give the same CGLMP probability are found to yield different CGLMP probabilities. However, violation of a CGLMP inequality based on any one of the possible quantum measurement sequences is sufficient to show that the Collins et al LHVT does not predict the same results as quantum theory. This is found to occur for a state considered in their paper - though for observables whose physical interpretation is unclear. In spite of the problems of comparing the HVT inequalities with quantum expressions, it is concluded that the CGLMP inequalities are indeed suitable for ruling out local hidden variable theories. The state involved could apply to a macroscopic system, so the CGLMP Bell inequalities are important for finding cases of macroscopic violations of Bell locality. Possible experiments in double-well Bose condensates involving atoms with two hyperfine components are discussed.
For decades, it has been known that local hidden variable theories cannot be disproved by collider experiments involving decaying particles. However, if these theories satisfy a small set of mild assumptions, they become testable. In particular, they can be disproved using Bell-like inequalities for μ+μ−μ^+ μ^-μ+μ− and τ+τ−τ^+ τ^-τ+τ− pairs.