Adaptive estimation and discrimination of Holevo-Werner channels

TL;DR

This paper analyzes the ultimate limits of estimating and discriminating Holevo-Werner channels, a class of quantum channels related to Werner states, using teleportation covariance and quantum information theory techniques.

Contribution

It provides the first analytical formulas for the quantum Chernoff bound and bounds on estimation precision for Holevo-Werner channels, extending previous methods to this class.

Findings

Computed the ultimate precision in parameter estimation of Holevo-Werner channels.

Derived an analytical formula for the quantum Chernoff bound for channel discrimination.

Bound the minimum error probability for discriminating two Holevo-Werner channels.

Abstract

The class of quantum states known as Werner states have several interesting properties, which often serve to illuminate unusual properties of quantum information. Closely related to these states are the Holevo-Werner channels whose Choi matrices are Werner states. Exploiting the fact that these channels are teleportation covariant, and therefore simulable by teleportation, we compute the ultimate precision in the adaptive estimation of their channel-defining parameter. Similarly, we bound the minimum error probability affecting the adaptive discrimination of any two of these channels. In this case, we prove an analytical formula for the quantum Chernoff bound which also has a direct counterpart for the class of depolarizing channels. Our work exploits previous methods established in [Pirandola and Lupo, PRL 118, 100502 (2017)] to set the metrological limits associated with this interesting class of quantum channels at any finite dimension.