Minimal sufficient positive-operator valued measure on a separable Hilbert space
Minimal sufficient positive-operator valued measure on a separable Hilbert space
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DOI：
10.1063/1.4934235
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发表时间：
2015-06
影响因子：
1.3
通讯作者：
Yui Kuramochi
中科院分区：
文献类型：
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作者：
Yui Kuramochi
我们引入了最小充分正算子值测度（POVM）的概念，它是在具有被测量子系统等价信息的POVM中冗余度最小的POVM.假设系统Hilbert空间是可分的，我们证明了对于一个给定的POVM，一个充分的统计称为Lehmann-Scheffe-Bahadur统计诱导一个最小的充分POVM。我们还表明，每个POVM有一个等价的最小充分POVM，这样的最小充分POVM是唯一的重新标记忽略空集。我们将这些结果应用于离散POVM和作者提出的信息守恒条件。
We introduce a concept of a minimal sufficient positive-operator valued measure (POVM), which is the least redundant POVM among the POVMs that have the equivalent information about the measured quantum system. Assuming the system Hilbert space to be separable, we show that for a given POVM, a sufficient statistic called a Lehmann-Scheffe-Bahadur statistic induces a minimal sufficient POVM. We also show that every POVM has an equivalent minimal sufficient POVM and that such a minimal sufficient POVM is unique up to relabeling neglecting null sets. We apply these results to discrete POVMs and information conservation conditions proposed by the author.