Interpolation by Different Types of Quantum Channels Using Conic Programs

TL;DR

This paper develops conic programming methods to interpolate various quantum channels, including those in convex sets, and demonstrates the existence of entanglement-breaking channels for specific matrix sets.

Contribution

It introduces conic programming techniques for quantum channel interpolation and generalizes results to convex sets, advancing quantum information processing methods.

Findings

Conic programs can produce different quantum channels as interpolation outputs.

Channels within convex sets can be obtained through generalized interpolation methods.

An entanglement-breaking channel exists for orthogonal input and output matrix sets.

Abstract

We have found conic programs for getting different types of quantum channels as outputs of interpolation problems. Afterwards, we have generalized our results for getting channels that belong to a convex set as outputs of the interpolation problem. We show the existence of an Entanglement breaking channel for orthogonal sets of input and output matrices.