量子态探测器设计：最坏情况下的最优后验性能
Quantum State Detector Design: Optimal Worst-Case a posteriori Performance
摘要：
所解决的问题是设计一种对特定量子态最敏感的探测器。在这里，我们集中在量子态检测使用最坏情况下的后验概率的检测作为设计标准。这个目标相当于问这样一个问题：如果检测器声明存在一个特定的状态，那么这个状态实际存在的概率是多少？我们表明，最大限度地提高这种最坏情况下的概率（最大限度地提高这种概率的最小可能值）是一个拟凸优化的矩阵的POVM（正算子值的措施），其特征在于测量仪器。我们还表明，与一个给定的POVM，优化是拟凸的矩阵特征的克劳斯算子和表示（OSR）在一个固定的基础。我们使用拉格朗日对偶理论建立确定性和随机检测的最优性条件。我们还研究了检测单个纯态的特殊情况。本文还讨论了凸优化用于量子态探测的数值方法。
英文摘要：
The problem addressed is to design a detector which is maximally sensitive to specific quantum states. Here we concentrate on quantum state detection using the worst-case a posteriori probability of detection as the design criterion. This objective is equivalent to asking the question: if the detector declares that a specific state is present, what is the probability of that state actually being present? We show that maximizing this worst-case probability (maximizing the smallest possible value of this probability) is a quasiconvex optimization over the matrices of the POVM (positive operator valued measure) which characterize the measurement apparatus. We also show that with a given POVM, the optimization is quasiconvex in the matrix which characterizes the Kraus operator sum representation (OSR) in a fixed basis. We use Lagrange Duality Theory to establish the optimality conditions for both deterministic and randomized detection. We also examine the special case of detecting a single pure state. Numerical aspects of using convex optimization for quantum state detection are also discussed.
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