Eventually entanglement breaking divisible quantum dynamics

TL;DR

The paper demonstrates that many quantum dynamical maps tend to become entanglement breaking over time, introducing the concept of eEB-divisibility where all propagators eventually break entanglement.

Contribution

It introduces the new concept of eEB-divisibility, showing its broad applicability to various quantum evolutions and its relation to entanglement breaking behavior.

Findings

Most quantum dynamical maps become entanglement breaking over time.

eEB-divisibility is a common property in quantum evolutions.

The concept links entanglement breaking to the structure of quantum dynamics.

Abstract

It is shown that a large class of quantum dynamical maps on complex matrix algebras governed by time-local Master Equations tend to become entanglement breaking in the course of time. Such situation seems to be generic for quantum evolution and in particular, completely positive dynamical semigroups with a unique faithful stationary state enjoy this property. Inspired by this observation, we propose a new concept of eventually entanglement breaking divisible (eEB-divisible) dynamics. A dynamical map is eEB-divisible if any propagator becomes entanglement breaking in finite time. It turns out that eEB-divisibility is quite general and holds for a large class of quantum evolutions.