论文标题
通过重复测量和三个规则进行量子状态歧视
Quantum State Discrimination via Repeated Measurements and the Rule of Three
论文作者
论文摘要
如果一个人可以访问相应的尖锐（投影值）测量值，那么对一组相互正交的纯状态的状态歧视任务是微不足道的，但是如果我们仅限于UNSHARP测量，该怎么办？鉴于任何现实的测量设备都会受到某些噪音的影响，因此值得考虑这样的问题。在本文中，我们考虑了以噪声测量的相互正交状态的最小误差状态歧视。我们表明，通过考虑在同一系统上的交换lüders测量的重复，我们可以增加成功区分状态的可能性。对于二进制lüders的测量，我们提供了任何数量重复的成功概率的全面表征。这使我们确定了“三个规则”，其中未从第二次测量中获得概率的变化，但是三分之一后有明显的改善。我们还为$ n $ n $值的交换性测量提供了部分结果，其中三个规则剩余的规则，但是二进制测量中存在的一般模式不再满足。
The task of state discrimination for a set of mutually orthogonal pure states is trivial if one has access to the corresponding sharp (projection-valued) measurement, but what if we are restricted to an unsharp measurement? Given that any realistic measurement device will be subject to some noise, such a problem is worth considering. In this paper we consider minimum error state discrimination for mutually orthogonal states with a noisy measurement. We show that by considering repetitions of commutative Lüders measurements on the same system we are able to increase the probability of successfully distinguishing states. In the case of binary Lüders measurements we provide a full characterisation of the success probabilities for any number of repetitions. This leads us to identify a 'rule of three', where no change in probability is obtained from a second measurement but there is noticeable improvement after a third. We also provide partial results for $N$-valued commutative measurements where the rule of three remains, but the general pattern present in binary measurements is no longer satisfied.
