Discrimination of bosonic dephasing quantum channels

TL;DR

This paper investigates methods to distinguish between two types of bosonic dephasing quantum channels, establishing bounds on error probabilities and extending the analysis from single to multiple uses.

Contribution

It provides new bounds on error probabilities for discriminating bosonic dephasing channels, including energy constraints and asymptotic multi-shot scenarios.

Findings

Unambiguous discrimination is impossible.

Derived upper bounds on error probability with energy constraints.

Extended results to multi-shot, asymptotic discrimination.

Abstract

We study the possibility of discriminating between two bosonic dephasing quantum channels. We show that unambiguous discrimination is not realizable. We then consider discrimination with nonzero error probability and minimize this latter in the absence of input constraints. In the presence of an input energy constraint, we derive an upper bound on the error probability. Finally, we extend these results from single-shot to multi-shot discrimination, envisaging the asymptotic behavior.