Sequential Quantum Channel Discrimination

TL;DR

This paper investigates the problem of sequential quantum channel discrimination, demonstrating exponential decay of error probabilities and highlighting the advantages of adaptive strategies and quantum memory in achieving optimal discrimination rates.

Contribution

It introduces a comprehensive analysis of adaptive and non-adaptive strategies, characterizes error decay rates, and explores the impact of quantum memory and measurements on discrimination performance.

Findings

Error probabilities decrease exponentially with the number of channel uses.

Adaptive strategies outperform non-adaptive ones in discrimination rates.

Quantum memory allows for higher achievable discrimination rates.

Abstract

We consider the sequential quantum channel discrimination problem using adaptive and non-adaptive strategies. In this setting the number of uses of the underlying quantum channel is not fixed but a random variable that is either bounded in expectation or with high probability. We show that both types of error probabilities decrease to zero exponentially fast and, when using adaptive strategies, the rates are characterized by the measured relative entropy between two quantum channels, yielding a strictly larger region than that achievable by non-adaptive strategies. Allowing for quantum memory, we see that the optimal rates are given by the regularized channel relative entropy. Finally, we discuss achievable rates when allowing for repeated measurements via quantum instruments and conjecture that the achievable rate region is not larger than that achievable with POVMs by connecting the result to the strong converse for the quantum channel Stein's Lemma.