On diagonal quantum channels

TL;DR

This paper investigates the structure of diagonal quantum channels, demonstrating their action on pure states as convex combinations and providing an algorithm to explicitly find their Kraus operators.

Contribution

It introduces an explicit algorithm for deriving Kraus operators of diagonal quantum channels and characterizes their action on pure states.

Findings

Diagonal quantum channels act as convex combinations on pure states.

An algorithm using Cholesky decomposition to find Kraus operators is proposed.

The structure of diagonal quantum channels is systematically characterized.

Abstract

In this paper we study diagonal quantum channels and their structure by proving some results and giving most applicable instances of them. Firstly, it is shown that action of every diagonal quantum channel on pure state from computational basis is a convex combination of pure states determined by some transition probabilities. Finally, by using the Cholesky decomposition it is presented an algorithmic method to find an explicit form for Kraus operators of diagonal quantum channels.