Dilation, Discrimination and Uhlmann's Theorem of Link Products of Quantum Channels

TL;DR

This paper advances the theoretical understanding of quantum channels by establishing dilation theorems for link products, analyzing channel discrimination improvements, and exploring Uhlmann's theorem in the context of diagonal channels.

Contribution

It introduces two new proofs of the Stinespring dilation theorem for link products and investigates the enhancement of channel distinguishability through self-linking.

Findings

Discrimination of quantum channels improves with repeated self-linking.

Maximum Uhlmann's theorem value is achieved for diagonal channels.

Two different methods are provided for the dilation theorem of link products.

Abstract

The study of quantum channels is the most fundamental theoretical problem in quantum information and quantum communication theory. The link product theory of quantum channels is an important tool for studying quantum networks. In this paper, we establish the Stinespring dilation theorem of the link product of quantum channels in two different ways, discuss the discrimination of quantum channels and show that the distinguishability can be improved by self-linking each quantum channel n times as n grows. We also find that the maximum value of Uhlmann's theorem can be achieved for diagonal channels.