Equivalence of qubit-environment entanglement and discord generation via pure dephasing interactions and the consequences thereof

TL;DR

This paper explores the relationship between qubit-environment entanglement and discord during pure dephasing, revealing that separable states are mostly discordant and highlighting implications for quantum evolution and channel classification.

Contribution

It establishes a link between entanglement and discord in pure dephasing, and demonstrates how local interactions can enhance entanglement despite being completely positive.

Findings

Separable qubit-environment states during pure dephasing have zero discord with respect to the environment.

Most separable states are discordant with respect to the qubit, but zero-discord states are possible in specific cases.

An example shows local, completely positive evolution can increase entanglement, challenging assumptions about local operations and classical communication (LOCC).

Abstract

We find that when a qubit initialized in a pure state experiences pure dephasing due to interaction with an environment, separable qubit-environment states generated during the evolution also have zero quantum discord with respect to the environment. What follows is that the set of separable states which can be reached during the evolution has zero volume and hence, such effects as sudden death of qubit-environment entanglement are very unlikely. In case of the discord with respect to the qubit, a vast majority of separable states qubit-environment is discordant, but in specific situations zero-discord states are possible. This is conceptually important since there is a connection between the discordance with respect to a given subsystem and the possibility of describing the evolution of this subsystem using completely positive maps. Finally, we use the formalism to find an exemplary evolution of an entangled state of two qubits that is completely positive, occurs solely due to interaction of only one of the qubits with its environment (so one could guess that it corresponds to a local operation, since it is local in a physical sense), but which nevertheless causes the enhancement of entanglement between the qubits. While this simply means that the considered evolution is completely positive, but does not belong to LOCC, it shows how much caution has to be exercised when identifying evolution channels that belong to that class.