Base norms and discrimination of generalized quantum channels

TL;DR

This paper introduces new norms in the space of hermitian operators related to the discrimination of generalized quantum channels, providing a framework for optimal quantum decision procedures and conditions for maximally entangled input states.

Contribution

It develops a novel class of base norms for hermitian operators and links them to quantum channel discrimination and decision problems, including optimality conditions.

Findings

Defined new norms related to quantum channel discrimination

Connected norms to maximal average payoff in decision problems

Established conditions for optimal 1-testers with maximally entangled inputs

Abstract

We introduce and study norms in the space of hermitian operators, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum states, channels and networks. We further introduce generalized quantum decision problems and show that the maximal average payoff of decision procedures is again given by these norms. We also study optimality of decision procedures, in particular, we obtain a necessary and sufficient condition under which an optimal 1-tester for discrimination of quantum channels exists, such that the input state is maximally entangled.