Unital Positive Maps and Quantum States

TL;DR

This paper investigates the structure of quantum states generated by unital completely positive maps, introduces a witness for states outside this subset, and explores the connection to quantum Perron-Frobenius theory.

Contribution

It provides a new framework for understanding unital positive maps, constructs a witness for non-membership, and links positive map representations to quantum Perron-Frobenius theory.

Findings

Construction of a witness certifying states outside the unital map subset

Analysis of positive map representations in quantum theory

Connection established between positive maps and quantum Perron-Frobenius theory

Abstract

We analyze the structure of the subset of states generated by unital completely positive quantum maps, A witness that certifies that a state does not belong to the subset generated by a given map is constructed. We analyse the representations of positive maps and their relation to quantum Perron-Frobenius theory.