Open quantum system approach to neutral Kaon interferometry

Abstract

Besides Heisenberg uncertainty, entanglement is another mechanism that can enforce complementarity in multipartite quantum systems. Analysing its effects in a bipartite system of two qubits, M. Jakob and J. Bergou had shown that the usual wave-particle duality relation, in interferometric systems, regarding which-way information and interference visibility, should be extended to a ¿triality¿ relation containing, in addition, a quantitative entanglement measure. Employing a model for the neutral K-meson propagation in free space in which its weak decay products are included as a second party, we study its effect in the neutral kaon interferometry. We show that a new quantitative triality relation can also be established in this case. The state of the total system remains pure in the course of dynamics, so, we can use the von Neumann entropy of a reduced party as a quantitative measure of entanglement. The other two quantities in the triality relation are the distinguishability between the decay products states corresponding to the two distinct kaon propagation modes KS and KL, and the wave-like path interference between these states. These two distinct modes are the analogues to the two separated paths in usual interferometric devices. The inequality obtained here can account for the complementarity between strangeness oscillations and lifetime information previously considered in the literature. Moreover, it allows us to visualise through the K0 ¿ K0 oscillations the fundamental role of entanglement in quantum complementarity.