Entanglement and entropy rates in open quantum systems

TL;DR

This paper investigates a conjecture relating the dynamics of quantum relative entropy and entanglement in open quantum systems, revealing conditions under which the conjecture holds or is violated through explicit solutions.

Contribution

It provides explicit solutions to a two-qubit Lindblad master equation and demonstrates when the conjectured entropy behavior is valid or violated based on initial and stationary states.

Findings

Conjecture holds for systems with separable asymptotic states.

Conjecture can be violated for systems with entangled asymptotic states.

Explicit two-qubit solutions illustrate the conditions for conjecture validity.

Abstract

We study a recent conjecture about the behavior of the quantum relative entropy compared to the relative entropy of entanglement in open bipartite systems. The conjecture states that, under a dissipative time-evolution, the positive rate of change of the relative entropy will always be larger than that of the relative entropy of entanglement. After explicitly solving a two-qubit master equation of Lindblad type with separable and entangled stationary states, we show that the conjecture can be violated for initial states with an entangled asymptotic state, while it appears to be confirmed when the asymptotic states are separable.