Characterization of affine automorphisms and ortho-order automorphisms of quantum probabilistic maps

TL;DR

This paper characterizes the structure-preserving bijective maps, specifically affine and ortho-order automorphisms, of quantum probabilistic maps using a Wigner-type theorem, enhancing understanding of quantum system symmetries.

Contribution

It provides a complete characterization of affine and ortho-order automorphisms of quantum probabilistic maps based on a Wigner-type theorem, advancing the mathematical understanding of quantum symmetries.

Findings

Characterization of affine automorphisms of quantum maps

Characterization of ortho-order automorphisms of quantum maps

Application of Wigner-type theorem to quantum automorphisms

Abstract

In quantum mechanics, often it is important for the representation of quantum system to study the structure-preserving bijective maps of the quantum system. Such maps are also called isomorphisms or automorphisms. In this note, using the Uhlhorn-type of Wigner's theorem, we characterize all affine automorphisms and ortho-order automorphisms of quantum probabilistic maps.