Finitely Repeated Adversarial Quantum Hypothesis Testing

TL;DR

This paper develops a quantum hypothesis testing framework for passive quantum detectors with finite samples, analyzing their asymptotic performance and applying results to quantum radar detection.

Contribution

It introduces a finite-sample quantum hypothesis testing approach under adversarial conditions, deriving exponential decay bounds for error probabilities.

Findings

Error bounds decay exponentially with the number of observations

Naive detectors achieve exponential decay in miss and false alarm rates

Miss rate decays slower than in non-adversarial quantum detection

Abstract

We formulate a passive quantum detector based on a quantum hypothesis testing framework under the setting of finite sample size. In particular, we exploit the fundamental limits of performance of the passive quantum detector asymptotically. Under the assumption that the attacker adopts separable optimal strategies, we derive that the worst-case average error bound converges to zero exponentially in terms of the number of repeated observations, which serves as a variation of quantum Sanov's theorem. We illustrate the general decaying results of miss rate numerically, depicting that the `naive' detector manages to achieve a miss rate and a false alarm rate both exponentially decaying to zero given infinitely many quantum states, although the miss rate decays to zero at a much slower rate than a quantum non-adversarial counterpart. Finally we adopt our formulations upon a case study of detection with quantum radars.