Computing the distance between quantum channels: Usefulness of the Fano representation

TL;DR

This paper introduces a Monte-Carlo algorithm leveraging the Fano representation to efficiently compute the diamond norm, a key measure of quantum channel distinguishability, demonstrated on single-qubit channels.

Contribution

It presents a novel Monte-Carlo method based on the Fano representation for calculating the diamond norm between quantum channels.

Findings

Efficient computation of the diamond norm using the proposed algorithm.

Application of the method to several single-qubit quantum channels.

The algorithm provides a physically transparent approach to quantum channel discrimination.

Abstract

The diamond norm measures the distance between two quantum channels. From an operational vewpoint, this norm measures how well we can distinguish between two channels by applying them to input states of arbitrarily large dimensions. In this paper, we show that the diamond norm can be conveniently and in a physically transparent way computed by means of a Monte-Carlo algorithm based on the Fano representation of quantum states and quantum operations. The effectiveness of this algorithm is illustrated for several single-qubit quantum channels.