论文标题
有限重复的对抗量子假设检验
Finitely Repeated Adversarial Quantum Hypothesis Testing
论文作者
论文摘要
我们根据有限样本量的设置，基于量子假设测试框架制定一个被动量子检测器。特别是，我们利用被动量子检测器渐近性能的基本限制。在假设攻击者采用可分离的最佳策略的假设下，我们得出，最坏情况下的平均误差约束在重复观测的数量方面呈指数级收敛，这是量子sanov定理的变化。我们在数值上说明了错率的总体衰减结果，描绘了“幼稚”检测器设法达到了失误率和错误的警报率，但指数均在无限的量子状态下呈成本衰减，尽管毫无数量的量子状态，但毫无疑问的速率降低到零的速度比量子非对方的速度较慢。最后，我们在用量子雷达的检测案例研究中采用我们的制剂。
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.
