Entanglement increase from local interactions which lead to non-positive local reduced dynamics

TL;DR

This paper investigates how local interactions with environments can lead to increased entanglement in bipartite quantum systems when the local dynamics are non-positive maps, challenging previous assumptions about entanglement behavior.

Contribution

It identifies conditions under which local non-positive maps can increase entanglement, and introduces a new procedure to generate such maps causing entanglement exceeding initial levels.

Findings

Entanglement can surpass initial values under local non-positive dynamics.

Standard completely positive maps do not increase entanglement.

A new method to produce local non-positive maps that enhance entanglement.

Abstract

Consider a bipartite quantum system S=AB such that each part interacts only with its local environment. Under such circumstances, one expects that the entanglement between parts A and B does not exceed its initial value during the time evolution. In fact, this is the case if the reduced dynamics of the system is given by $\mathcal{E}_{A}\otimes \mathcal{E}_{B}$, where $\mathcal{E}_{A}$ and $\mathcal{E}_{B}$ are quantum channels, i.e., completely positive trace-preserving maps. But, the reduced dynamics of the system may be given by a map as $\Psi_{A}\otimes \Psi_{B}$, where $\Psi_{A}$ and $\Psi_{B}$ are local non-positive maps. Then, the entanglement between A and B can exceed its initial value, as was shown in the case studied by Jordan et al. [Phys. Rev. A 76, 022102 (2007)]. In this paper, we first explore the general circumstances under which one can find such cases as they found. Next, we introduce another general procedure which leads to local non-positive maps that cause entanglement exceeding.