A Note on Resistance of NPT to Mixture of Separable States

TL;DR

This paper investigates how the negative partial transpose (NPT) property of pure entangled states remains stable when mixed with a limited number of separable states, extending the analysis to multipartite systems.

Contribution

It provides a bound on the number of separable states that can be mixed with an NPT pure state without losing its NPT property, generalizing previous results to multipartite states.

Findings

NPT property persists when mixed with up to 777-1 separable states for bipartite states.

The stability result is extended to multipartite pure states.

The bound depends on the Schmidt number of the state.

Abstract

We study the stability of NPT property of an arbitrary pure entangled state under the mixture of arbitrary pure separable states. For bipartite pure states with Schmidt number $n$ $(n>1)$ which is NPT, we show that this state is still NPT when it is mixed with no more than $\frac{n(n-1)}{2}-1$ arbitrary pure separable states. This result is generalized to multipartite case.