Extremal Channels for a genaral Quantum system

TL;DR

This paper characterizes extremal quantum channels for N-level systems, providing parameterizations and representations for systems with 2, 3, and 4 levels, advancing understanding of quantum channel structure.

Contribution

It introduces a parameterization of extremal quantum channels for N-level systems, including explicit representations for N=2, 3, 4, enhancing the mathematical understanding of quantum channels.

Findings

Extremal channels are characterized by N^2 - N real parameters.

Explicit representations are provided for N=2, 3, 4.

The parameterization involves rotations and convex sums of extremal channels.

Abstract

Quantum channels can be mathematically represented as completely positive trace-preserving maps that act on a density matrix. A general quantum channel can be written as a convex sum of `extremal' channels. We show that for an $N$-level system, the extremal channel can be characterized in terms of $N^2$-$N$ real parameters coupled with rotations. We give a representation for $N$= 2, 3, 4.