Query complexities of quantum channel discrimination and estimation: A unified approach

TL;DR

This paper develops a unified framework for analyzing the query complexities of quantum channel discrimination and estimation, providing new lower bounds and simplifying proofs using isometric extensions.

Contribution

It introduces a unified approach to establish lower bounds on query complexity, applying isometric extensions and unifying existing results in quantum channel discrimination and estimation.

Findings

Established new lower bounds on query complexity.

Provided simplified proofs using isometric extensions.

Unified existing bounds within a common framework.

Abstract

The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one must call an unknown channel to identify it within a desired threshold on the error probability. In this paper, we establish lower bounds on the query complexities of channel discrimination and estimation, in both the parallel and adaptive access models. We do so by establishing new or applying known upper bounds on the squared Bures distance and symmetric logarithmic derivative Fisher information of channels. Phrasing our statements and proofs in terms of isometric extensions of quantum channels allows us to give conceptually simple proofs for both novel and known bounds. We also provide alternative proofs for several established results in an effort to present a consistent and unified framework for quantum channel discrimination and estimation, which we believe will be helpful in addressing future questions in the field.