Robustness of entangled states that are positive under partial transposition

TL;DR

This paper investigates the stability of bipartite PPT entangled states under small perturbations, showing most are unconditionally robust and providing explicit bounds on the volume of such states.

Contribution

It demonstrates that nearly all PPT entangled states are unconditionally robust and constructs explicit examples of open balls containing these states, offering volume bounds.

Findings

Most PPT entangled states are unconditionally robust.

Explicit construction of open PPT entangled balls with finite radii.

Provides a lower bound on the volume of PPT entangled states.

Abstract

We study robustness of bipartite entangled states that are positive under partial transposition (PPT). It is shown that almost all PPT entangled states are unconditionally robust, in the sense, both inseparability and positivity are preserved under sufficiently small perturbations in its immediate neighborhood. Such unconditionally robust PPT entangled states lie inside an open PPT entangled ball. We construct examples of such balls whose radii are shown to be finite and can be explicitly calculated. This provides a lower bound on the volume of all PPT entangled states. Multipartite generalization of our constructions are also outlined.