Finitely Repeated Adversarial Quantum Hypothesis Testing

Abstract

Quantum technologies have been considered as a method to enhance cyber-security due to the unique properties of quantum systems. However, quantum systems themselves could also suffer from strategic attacks. In this paper, we formulate the relationship between the strategic attacker and a passive quantum detector into a Stackelberg game. By deriving the optimal detection rule at equilibrium, we study the detection performance of the detector under the setting of finite sample size of corrupted observations. Under mild assumptions, we show that the miss. We illustrate the general decaying results of the miss rate numerically, depicting that the passive detector manages to achieve a miss rate and a false alarm rate both exponentially decaying to zero given infinitely many quantum states, although 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.