Completely positive completely positive maps (and a resource theory for non-negativity of quantum amplitudes)

TL;DR

This paper explores quantum states with non-negative amplitudes and the channels that preserve them, introducing a resource theory framework to quantify their non-negativity as a quantum resource.

Contribution

It defines and studies completely positive completely positive channels and develops a resource theory for non-negativity of quantum amplitudes.

Findings

Characterization of channels preserving non-negative quantum states

Development of a resource measure for non-negativity

Insights into the structure of non-negative quantum states

Abstract

In this work we examine quantum states which have non-negative amplitudes (in a fixed basis) and the channels which preserve them. These states include the ground states of stoquastic Hamiltonians and they are of interest since they avoid the Sign Problem and can thus be efficiently simulated. In optimization theory, the convex cone generated by such states is called the set of completely positive (CP) matrices (not be confused with completely positive superoperators). We introduce quantum channels which preserve these states and call them completely positive completely positive. To study these states and channels, we use the framework of resource theories and investigate how to measure and quantify this resource.