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Chinese Physics C

Testing Bell inequality at experiments of high energy physics

X. Q. Hao, 柯红卫, 丁亦兵, 沈彭年, 李学潜

Published Jan 1, 2010• 0 citations
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Abstract

Besides using the laser beam, it is very tempting to directly testify the Bell inequality at high energy experiments where the spin correlation is exactly what the original Bell inequality investigates. In this work, we follow the proposal raised in literature and use the successive decays J/ψ→γηc→Λ...

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Besides using the laser beam, it is very tempting to directly testify the Bell inequality at high energy experiments where the spin correlation is exactly what the original Bell inequality investigates. In this work, we follow the proposal raised in literature and use the successive decays J/ψ → γη c → Λ → pπ − π + to testify the Bell inequality. Our goal is twofold, namely, we first make a Monte–Carlo simulation of the processes based on the quantum field theory (QFT). Since the underlying theory is QFT, it implies that we pre-admit the validity of quantum picture. Even though the QFT is true, we need to find how big the database should be, so that we can clearly show deviations of the correlation from the Bell inequality determined by the local hidden variable theory. There have been some critiques on the proposed method, so in the second part, we suggest some improvements which may help to remedy the ambiguities indicated by the critiques. It may be realized at an updated facility of high energy physics, such as BES III.
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.
This paper discusses the feasibility of testing Bell's inequality with the charmonium decays |ηc→ΛΛ‾\eta _{\mathrm {c}} \rightarrow \Lambda \overline {\Lambda }ηc​→ΛΛ|⁠, |χc0→ΛΛ‾\chi _{{\mathrm {c}}0} \rightarrow \Lambda \overline {\Lambda }χc0​→ΛΛ| and |J/ψ→ΛΛ‾{\mathrm {J}}/\psi \rightarrow \Lambda \overline {\Lambda }J/ψ→ΛΛ|⁠. We develop a new formulation of Bell's inequality represented with particles’ orientations, which can be measured straightforwardly in experiment, and seek to ascertain if it is violated in these decay processes. It is shown that the ηc channel and the |χc0\chi _{c0}χc0​| channel maximally violate Bell's inequality, while the |${\mathrm {J}}/\psi $| channel gives no inconsistency with it. Simulations dealing with experimental aspects are also implemented. The expected statistical fluctuations and achievable significance are estimated as a function of sample size.
Introduction Annus mirabilis 1964 1964 was a wonderful year for physics. In this annus mirabilis, summarising and simplifying a little, the quark model was proposed by Gell-Mann and Zweig and charm and colour properties were introduced, Higgs published his work on the scalar boson, the _ boson and CP violation were discovered, cosmic background radiation was identified and, finally, Bell inequalities were suggested. Most of these works were later subjects of a Nobel prize. Unluckily John Bell left us too early for this achievement, but, at least in my opinion, his work [1] is probably the most fruitful among all these huge advances, since now we can recognise that it was the root of a fundamental change in our vision of the physical world, providing, on one hand, the possibility of a test of quantum mechanics against a whole class of theories (substantially all the theories that we could define as “classical”) and, on the other hand, introducing a clear notion of quantum nonlocality that represents not only a challenge in understanding quantum mechanics, but also one of the most important resources paving the way to quantum technologies that were developed in the last decades based on the quantum correlations discussed in the Bell paper. In the following we will present the experimental progress in testing Bell inequalities. Rather amazingly even 50 years after Bell's paper, a conclusive test of his proposal is still missing [2, 3]. Nevertheless, huge progress has been achieved with respect to the first experiments.We will discuss these developments and the remaining problems for a conclusive test of Bell inequalities in detail. The Bell Inequalities, Their Hypotheses and the Experimental Loopholes In order to understand the experimental difficulties in achieving a final test of Bell inequalities, let us analyse a little how these inequalities are derived and the explicit and implicit hypotheses they contain. The proof of Bell inequalities usually starts by considering two separated subsystems of an entangled state, which are addressed to two independent measurement apparatuses measuring the expectation values of two dichotomic observables, Aa and B b . a, b are two parameters describing the settings of the measuring apparatus A and B , respectively.
Bell's theorem is an important milestone in the development of quantum mechanics. It draws a line between concepts such as realism and locality on the one hand and quantum mechanics on the other. Experimentally veried violations of Bell inequalities can yield important information about what assumptions can be made about physical reality. Experiments have been conducted for over 40 years, but have left loopholes open in their executions. It is of great interest to close these loopholes, and in order to do so, further experiments are needed. The objective of this project is to investigate the underlying, previous work in the eld and to formulate a proposal for a new experiment. To do this, the derivations of the original Bell inequality and the CHSH inequality are presented along with previously conducted experiments. Also presented is the EPR paradox from which sprung the original Bell inequality.