On Random Unitary Channels

TL;DR

This paper characterizes when a quantum channel can be expressed as a mixture of unitary operations and introduces a distance measure to compare channels with random unitary maps, aiding in understanding quantum errors.

Contribution

It provides necessary and sufficient conditions for decomposing CPT maps into convex combinations of unitaries and proposes a method to measure the distance to the set of random unitary channels.

Findings

Derived conditions for decomposability into unitary maps

Proposed a distance measure for CPT maps

Facilitates distinguishing classical and non-classical errors

Abstract

In this article we provide necessary and sufficient conditions for a completely positive trace-preserving (CPT) map to be decomposable into a convex combination of unitary maps. Additionally, we set out to define a proper distance measure between a given CPT map and the set of random unitary maps, and methods for calculating it. In this way one could determine whether non-classical error mechanisms such as spontaneous decay or photon loss dominate over classical uncertainties, for example in a phase parameter. The present paper is a step towards achieving this goal.