Local PT-symmetric evolutions on separable states and violation of no-signaling

TL;DR

This paper demonstrates that local PT-symmetric quantum evolutions can violate the no-signaling principle for certain states, but such violations can be mitigated by adopting a CPT inner product.

Contribution

It reveals how PT-symmetric evolutions impact the no-signaling principle and proposes a solution using a CPT inner product to restore it.

Findings

Violations occur for separable and classically correlated states.

Certain PT-symmetric operations can preserve no-signaling.

Using a CPT inner product removes violations.

Abstract

We show that local PT-symmetric evolutions can lead to violation of the no-signaling principle for separable and even classically correlated bipartite shared quantum states. For classically correlated states, specially chosen PT-symmetric operations from a set of zero volume can also preserve the principle. The violations can be removed by using a CPT inner product instead of the traditional one.