Open-quantum-systems approach to complementarity in neutral-kaon interferometry

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 KS, KL, 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 -K 0 oscillations the fundamental role of entanglement in quantum complementarity.

Complementary Resource Relation of Concurrence and Roughness for atwo Qubits State

“…The main advantage is that the axis variables can be considered such as quantum resources. This is similar to the complementarity relation for a bipartite system exposed to an interferometer [15], and its generalization for open systems [16,17]. Fan and collaborators [18] have shown a complementary relation for quantum coherence and quantum correlations.…”

Simulation of Afshar's Double Slit Experiment

“…These relations are relevant to quantum computing as they identify the relationship between quantum resources [15,16]. For open systems, as in real experiments, the validity of the complementarity relations is limited [17,18,19]. Within this context, we hope that our analysis of Afshar's attack underlines the importance of duality relationships.…”