Convex decomposition of dimension-altering quantum channels

TL;DR

This paper investigates the convex structure of dimension-altering quantum channels, providing circuit representations and a decomposition scheme to express arbitrary channels as convex sums of extreme channels, with numerical validation.

Contribution

It introduces a method to decompose dimension-altering quantum channels into convex sums of extreme channels using quantum circuit representations, advancing understanding of their convex structure.

Findings

Numerical simulations validate the decomposition scheme.

Circuit representations enable practical optimization for channel decomposition.

The study enhances the understanding of convex properties of dimension-altering channels.

Abstract

Quantum channels, which are completely positive and trace preserving mappings, can alter the dimension of a system; e.g., a quantum channel from a qubit to a qutrit. We study the convex set properties of dimension-altering quantum channels, and particularly the channel decomposition problem in terms of convex sum of extreme channels. We provide various quantum circuit representations of extreme and generalized extreme channels, which can be employed in an optimization to approximately decompose an arbitrary channel. Numerical simulations of low-dimensional channels are performed to demonstrate our channel decomposition scheme.