Uncertainty relations for positive-operator-valued measures
Uncertainty relations for positive-operator-valued measures
复制标题
正算子值测度的不确定性关系
DOI：
10.1103/physreva.76.042114
复制
发表时间：
2007
影响因子：
2.9
通讯作者：
S. Massar
中科院分区：
文献类型：
--
作者：
S. Massar
有多少不可避免的随机性是由一个正算子值测量（POVM）产生的？我们使用两种互补的方法来解决这个问题。首先，我们研究了与POVM结果相关的实变量的方差。在这种情况下，我们引入一个不确定性算子，它测量通过执行POVM而不是冯·诺伊曼测量引入了多少额外的噪声。我们通过研究自旋为1/2的粒子{sigma}{下标x}和{sigma}{下标z}的联合估计的方差来说明第一种方法。我们证明，对于无偏测量，这些方差的和下界为1。在我们的第二种方法中，我们研究POVM结果的熵。特别是，我们试图建立POVM结果熵的下界。我们通过示例说明第二种方法。
How much unavoidable randomness is generated by a positive-operator-valued measure (POVM)? We address this question using two complementary approaches. First, we study the variance of a real variable associated with the POVM outcomes. In this context we introduce an uncertainty operator which measures how much additional noise is introduced by carrying out a POVM rather than a von Neumann measurement. We illustrate this first approach by studying the variances of joint estimates of {sigma}{sub x} and {sigma}{sub z} for spin-1/2 particles. We show that for unbiased measurements the sum of these variances is lower bounded by 1. In our second approach we study the entropy of the POVM outcomes. In particular, we try to establish lower bounds on the entropy of the POVM outcomes. We illustrate this second approach by examples.