Study of temporal quantum correlations in decohering B and K meson systems

TL;DR

This paper investigates how quantum correlations in B and K meson systems are affected by decoherence and CP violation, demonstrating violations of Leggett-Garg inequalities and proposing LG-type parameters as effective measures.

Contribution

It introduces a detailed analysis of temporal quantum correlations in meson systems incorporating decoherence and CP violation effects, highlighting LG-type parameters as practical observables.

Findings

LG inequality is violated in B and K mesons, especially in K mesons.

Decoherence reduces the extent of LGI violation.

LG-type parameters can be directly expressed in terms of transition probabilities.

Abstract

In this work we study temporal quantum correlations, quantified by Leggett-Garg (LG) and LG-type inequalities, in the $B$ and $K$ meson systems. We use the tools of open quantum systems to incorporate the effect of decoherence which is quantified by a single phenomenological parameter. The effect of $CP$ violation is also included in our analysis. We find that the LG inequality is violated for both $B$ and $K$ meson systems, the violation being most prominent in the case of $K$ mesons and least for $B_s$ system. Since the systems with no coherence do not violate LGI, incorporating \textit{decoherence} is expected to decrease the extent of violation of LGI and is clearly brought out in our results. We show that the expression for the LG functions depends upon an additional term, apart from the experimentally measurable meson transition probabilities. This term vanishes in the limit of zero decoherence. On the other hand, the LG-type parameter can be directly expressed in terms of transition probabilities, making it a more appropriate observable for studying temporal quantum correlations in neutral meson systems.