Excluding false negative error in certification of quantum channels

TL;DR

This paper investigates conditions under which false negative errors can be eliminated in quantum channel certification, providing bounds on query numbers and comparing parallel and adaptive schemes.

Contribution

It establishes conditions for excluding false negative errors after finite queries, introduces a class of channels with this property, and compares parallel and adaptive certification schemes.

Findings

False negative errors can be excluded under certain conditions.

Parallel schemes are sufficient for certification, but adaptive schemes can reduce steps.

A class of channels allows exclusion of false negatives without unambiguous distinction.

Abstract

Certification of quantum channels is based on quantum hypothesis testing and involves also preparation of an input state and choosing the final measurement. This work primarily focuses on the scenario when the false negative error cannot occur, even if it leads to the growth of the probability of false positive error. We establish a condition when it is possible to exclude false negative error after a finite number of queries to the quantum channel in parallel, and we provide an upper bound on the number of queries. On top of that, we found a class of channels which allow for excluding false negative error after a finite number of queries in parallel, but cannot be distinguished unambiguously. Moreover, it will be proved that parallel certification scheme is always sufficient, however the number of steps may be decreased by the use of adaptive scheme. Finally, we consider examples of certification of various classes of quantum channels and measurements.