The automorphism group of separable states in quantum information theory

TL;DR

This paper characterizes the automorphism group of separable states in quantum information theory, showing it is generated by natural transformations like basis changes, partial transpose, and tensor factor interchange.

Contribution

It identifies the generators of the automorphism group of separable states, providing a complete description of their structure in quantum information theory.

Findings

Automorphism group of separable states is generated by natural automorphisms.

Change of basis, partial transpose, and tensor factor interchange are key automorphisms.

Results apply to preservers of the product numerical range.

Abstract

We show that the linear group of automorphism of Hermitian matrices which preserves the set of separable states is generated by \emph{natural} automorphisms: change of an orthonormal basis in each tensor factor, partial transpose in each tensor factor, and interchanging two tensor factors of the same dimension. We apply our results to preservers of the product numerical range.