Discrimination of the change point in a quantum setting
Discrimination of the change point in a quantum setting
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DOI：
10.1103/physreva.83.052328
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发表时间：
2011-05-27
影响因子：
2.9
通讯作者：
Hayashi, Masahito
中科院分区：
文献类型：
--
作者：
Akimoto, Daiki;Hayashi, Masahito
在变点问题中，我们确定观察到的分布何时变为另一个分布。我们将这个问题扩展到一个量子的情况下，一个未知的纯态的副本正在分发。也就是说，我们估计分布量子纯态何时改变。作为最基本的情况，我们处理在两个给定的候选t（1）和t（2）之间确定真正的变点t（c）的问题。我们的问题在数学上等同于当提供多个状态副本时，用两个未知状态中的一个来识别给定状态。在初始和最终量子纯态服从不变先验的情况下，给出了平均错误概率的最小值，并给出了获得平均错误概率的最优正算子值测度（POVM）.当初始和最终量子纯态固定时，我们还计算了在上述POVM下判定变点的错误概率。这些分析结果使我们能够在渐近情况下计算值。
In the change point problem, we determine when the observed distribution has changed to another one. We expand this problem to a quantum case where copies of an unknown pure state are being distributed. That is, we estimate when the distributed quantum pure state is changed. As the most fundamental case, we treat the problem of deciding the true change point t(c) between the two given candidates t(1) and t(2). Our problem is mathematically equal to identifying a given state with one of the two unknown states when multiple copies of the states are provided. The minimum of the averaged error probability is given and the optimal positive operator-valued measure (POVM) is given to obtain it when the initial and final quantum pure states are subject to the invariant prior. We also compute the error probability for deciding the change point under the above POVM when the initial and final quantum pure states are fixed. These analytical results allow us to calculate the value in the asymptotic case.