Bounds on the breaking time for entanglement-breaking channels

TL;DR

This paper investigates the timing of entanglement breaking in quantum channels under Lindblad dynamics, deriving bounds on when entanglement is lost using quantum speed limits and entanglement witnesses.

Contribution

It introduces a method to estimate lower bounds on entanglement breaking times for dynamical quantum channels, connecting the bounds to the dynamics alone.

Findings

Derived lower bounds on entanglement breaking times.

Bound expressions depend on input states, dynamical maps, and witnesses.

Special cases relate bounds directly to dynamical characteristics.

Abstract

Entanglement-breaking channels are quantum channels transforming entangled states to separable states. Despite a detailed discussion of their operational structure, to be found in the literature, studies on dynamical characteristics of this type of maps are yet limited. We consider one of the basic questions: for Lindblad-type dynamics, when does a given channel break entanglement? We discuss the finite-dimensional case where the quantification of entanglement via entanglement witnesses is utilized. For the general setup, we use the method of quantum speed limit to derive lower bounds on entanglement breaking times in terms of an input state, the dynamical map and the witness operator. Then, with a particular choice of the input state and the entanglement witness, the bounds for the breaking time are turned to solely reflect the characteristics of the dynamics.