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Particle Physics—Bell Inequalities

Reinhold A. Bertlmann, Nicolai Friis

Published Sep 7, 2023• 0 citations
Publisher

Abstract

Abstract In this chapter we review the phenomenology of K mesons, or kaons, and the possibility of Bell-inequality violation in systems of K-meson pairs. To this end we first study their properties and features: strangeness represented by the strange quark, the violation of the charge-conjugation parity (CP) symmetry, strangeness oscillation, and regeneration. These interesting phenomena emerge from the fact that the strangeness eigenstates, CP eigenstates, and mass eigenstates are not the same, as well as from the interplay of the strangeness-conserving and CP-conserving strong interaction and the weak interaction which violates these conservation rules. We then examine the quasi-spin analogy of K mesons and the correlation functions for entangled K-meson pairs. After concluding that the physical measurements possible for K-mesons do not allow a direct violation of Bell inequalities such as the Uchiyama-Bell inequality we identify the CP violation as an indirect violation of Bell inequalities.

DOI
10.1093/oso/9780199683338.003.0026

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Abstract In this chapter we review the phenomenology of K mesons, or kaons, and the possibility of Bell-inequality violation in systems of K-meson pairs. To this end we first study their properties and features: strangeness represented by the strange quark, the violation of the charge-conjugation parity (CP) symmetry, strangeness oscillation, and regeneration. These interesting phenomena emerge from the fact that the strangeness eigenstates, CP eigenstates, and mass eigenstates are not the same, as well as from the interplay of the strangeness-conserving and CP-conserving strong interaction and the weak interaction which violates these conservation rules. We then examine the quasi-spin analogy of K mesons and the correlation functions for entangled K-meson pairs. After concluding that the physical measurements possible for K-mesons do not allow a direct violation of Bell inequalities such as the Uchiyama-Bell inequality we identify the CP violation as an indirect violation of Bell inequalities.
The nonlocal property of quantum mechanics can be nicely tested in high energy physics; in particular, the neutral kaon pairs as produced at DAΦΦΦNE, Frascati, are very well suited. The analogies of kaons as compared to polarized photons or spin--1/2 particles --the kaonic qubit feature-- are reviewed. However, there are also fundamental differences which occur due to the kaon time evolution and due to internal symmetries; in particular, the violation of CP symmetry is related to the violation of Bell inequalities. Two type of Bell inequalities for kaons are presented, one for the variation of the ``quasi--spin'' and the other for different detection times of the kaon.
This chapter provides an in-depth analysis of the properties and phenomena associated with neutral K-mesons. Kaons are quantum systems illustrating strange behaviors. We begin by examining the significance of strangeness and charge parity violation in understanding these particles. The concept of strangeness oscillations is then introduced, explaining oscillations between K0 and K¯0 states. The regeneration of KS is investigated, uncovering the underlying mechanisms involved. The discussion moves on to quasi-spin space, exploring its bases and their implications. The entangled states of kaon pairs K0K¯0 are considered, with a focus on maximally entangled neutral kaons and nonmaximally entangled states. Decoherence effects on entangled kaons are examined, utilizing the density matrix description to capture the dynamics. A dedicated decoherence parameter is introduced to quantify the impact of decoherence. Furthermore, the chapter investigates the loss of entanglement through measures such as von Neumann entanglement entropy, entanglement of formation, and concurrence. These measures provide insights into quantifying and characterizing entanglement in the context of neutral kaons. Through this comprehensive exploration of properties, phenomena, and entanglement dynamics, this chapter aims to pointing out recent works on neutral kaons, contributing to advancements in particle physics.
In 1964 the physicists John St. Bell working at CERN took the 1935-idea of Einstein-Podolsky-Rosen seriously and found that all theories based on local realism have to satisfy a certain inequality, nowadays dubbed Bell’s inequality. Experiments with ordinary matter systems or light show violations of Bell’s inequality favouring the quantum theory though a loophole free experiment has not yet been performed. This contribution presents an experimentally feasible Bell inequality for systems at higher energy scales, i.e. entangled neutral Ҡ -meson pairs that are typically produced in Φ -mesons decays or proton-antiproton annihilation processes. Strong requirements have to be overcome in order to achieve a conclusive tests, such a proposal was recently published. Surprisingly, this new Bell inequality reveals new features for weakly decaying particles, in particular, a strong sensitivity to the combined charge-conjugation-parity (CP) symmetry. Here-with, a puzzling relation between a symmetry breaking for mesons and Bell’s inequality—which is a necessary and sufficient condition for the security of quantum cryptography protocols— is established. This becomes the more important since CP symmetry is related to the cosmological question why the antimatter disappeared after the Big Bang.
Abstract In this chapter we revisit the creation of an entangled kaon state where the particles comprising the relevant pair propagate in to opposite directions. Experimental tests of Bell inequalities in particle physics are difficult and feature loopholes for local realistic models. Although such Bell tests are of fundamental interest, the examination of entanglement rather than non-locality for meson-antimeson pairs might be more feasible. To examine the possibilities and challenges for such tests, it is useful to study possible mechanisms for decoherence that might influence the quality of the entanglement. We consider possible decoherence effects arising from interactions of the quantum system with its environment: strong-interaction scatterings of kaons with nucleons, weak-interaction decays, as well as experimental noise. We concentrate on a specific model of decoherence developed by Bertlmann and Grimus that allows us to quantify the strength of such possible decoherence effects by the data of existing experiments
Abstract It has been well established that quantum mechanics (QM) violates Bell inequalities (BI), which are consequences of local realism (LR). Remarkably QM also violates Leggett inequalities (LI), which are consequences of a class of nonlocal realism called crypto-nonlocal realism (CNR). Both LR and CNR assume that measurement outcomes are determined by preexisting objective properties, as well as hidden variables (HV) not considered in QM. We extend CNR and LI to include the case that the measurement settings are not externally fixed, but determined by HV. We derive a new version of LI, which is then shown to be violated by entangled BdB_dBd​ B d mesons, if charge–conjugation–parity (CP) symmetry is indirectly violated, as indeed established. The experimental result is quantitatively estimated by using the indirect CP violation parameters, and the maximum of a suitably defined relative violation is about 2.7%2.7\%2.7% 2.7 % . Our work implies that particle physics violates CNR. Our LI can also be tested in other systems such as photon polarizations.
The decays of the B meson into vector mesons, observed during the LHCb experiment, provide an ideal laboratory to investigate particle physics phenomena with quantum information theory methods. In this article, we focus on the decays yielding a pair of ϕ mesons to investigate the presence of entanglement in the spin correlations of the system and quantify the amount of Bell inequality violation it entails. Our results show that the present LHCb data allow access to entanglement and to the Bell inequality violation with a significance exceeding the 5σ threshold in both the cases. This demonstrates that the strong and electroweak interactions responsible for the B meson decay act as a source of entanglement and the quantum mechanics nature of high-energy phenomena. Particular attention is paid to the assessment of loopholes: deficiencies in the experimental setup which could invalidate the results of the Bell test.