Conditions for optimal input states for discrimination of quantum channels

TL;DR

This paper establishes optimality conditions for quantum channel discrimination using semidefinite programming, highlighting the importance of input state entanglement and providing error estimates when maximally entangled states are suboptimal.

Contribution

It introduces new optimality conditions for quantum channel discrimination, emphasizing the role of input state entanglement and analyzing cases where maximally entangled states are not optimal.

Findings

Optimality conditions derived using semidefinite programming.

Maximally entangled states are not always optimal input states.

Error estimates provided for non-maximally entangled input states.

Abstract

We find optimality conditions for testers in discrimination of quantum channels. These conditions are obtained using semidefinite programming and are similar to optimality conditions for POVMs obtained by Holevo for ensembles of quantum states. We get a simple condition for existence of an optimal tester with any given input state with maximal Schmidt rank, in particular with a maximally entangled input state and we show the pitfalls of using input states with not maximal Schmidt rank. In case when maximally entangled state is not the optimal input state an error estimate is obtained. The results for maximally entangled input state are applied to covariant channels, qubit channels, unitary channels and simple projective measurements.