An open quantum system approach to complementarity in neutral kaon interferometry

TL;DR

This paper applies an open quantum system approach to analyze wave-particle duality and entanglement in neutral kaon interferometry, introducing a new quantitative 'triality' relation that links distinguishability, interference, and entanglement.

Contribution

It extends the concept of quantum complementarity to kaon-antikaon oscillations using an open system framework, revealing a new quantitative relation involving entanglement.

Findings

A new 'triality' relation for kaon systems is established.

Entanglement influences the complementarity between strangeness oscillations and lifetime information.

The approach visualizes the role of entanglement in quantum interference phenomena.

Abstract

In bipartite quantum systems, entanglement correlations between the parties exerts direct influence in the phenomenon of wave-particle duality. This effect has been quantitatively analyzed in the context of two qubits by M. Jakob and J. Bergou [Optics Communications 283(5) (2010) 827]. Employing a description of the $K$-meson propagation in free space where its weak decay states are included as a second party, we study here this effect in the kaon-antikaon oscillations. We show that a new quantitative "triality" relation holds, similar to the one considered by Jakob and Bergou. In our case, it relates the distinguishability between the decay products states corresponding to the distinct kaon propagation modes $K_S $, $K_L $, the amount of wave-like path interference between these states, and the amount of entanglement given by the reduced von Neumann entropy. The inequality can account for the complementarity between strangeness oscillations and lifetime information previously considered in the literature, therefore allowing one to see how it is affected by entanglement correlations. As we will discuss, it allows one to visualize clearly through the $K^{0}$$\overline{K}\,^{0}$ oscillations the fundamental role of entanglement in quantum complementarity.