Classification of the separable maps which preserve Werner states

TL;DR

This paper classifies certain quantum maps that preserve Werner states and commute with specific unitaries, providing insights into their implementability and implications for entanglement manipulation.

Contribution

It provides a complete classification of separable, Werner-preserving maps and establishes conditions for their implementation via SLOCC, linking PPT-preserving maps to SLOCC implementability.

Findings

All PPT-preserving maps can be implemented by SLOCC.

Werner state entanglement cannot be increased stochastically, even with PPT entanglement.

A simple condition for implementability by SLOCC was derived.

Abstract

We classify the completely-positive maps acting on two $d$-dimensional systems which commute with all $U\otimes U$ unitaries, where $U\in SU(d)$. This set of operations map Werner states to Werner states. We find a simple condition for a map being implementable by stochastic local operations and classical communication (SLOCC). We show that all PPT-preserving maps can be implemented by SLOCC. This can be used to prove that the entanglement of Werner states cannot be stochastically increased, even if we allow PPT entanglement for free.