Excluding false negative error in certification of quantum channels

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.

Discrimination and certification of unknown quantum measurements

“…Advantage of using entangled states for minimumerror discrimination of quantum channels was studied in [5,6]. General conditions when quantum channels can be discriminated in the minimum error, unambiguous and asymmetric scenarios were derived in [7], [8] and [9] respectively. Another formalism used for for studying discrimination of quantum channels is based on process POVM (PPOVM) [10].…”