Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures
Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures
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DOI：
10.1103/physreva.78.052119
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发表时间：
2008-11-01
影响因子：
2.9
通讯作者：
Imai, Hideki
中科院分区：
文献类型：
--
作者：
Miyadera, Takayuki;Imai, Hideki
讨论了两个任意正算子值测度同时测量的一个限制。一般说来，同时测量两个非对易可观仅是大致可能的。在沃纳公式的基础上，我们引入了一个能观量之间的距离来量化测量的精确度。我们推导出一个将可达到的精度与两个观测值之间的非对易性联系起来的不等式。作为副产品，得到了两个正算子值测度同时可测的必要条件。
A limitation on simultaneous measurement of two arbitrary positive-operator-valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation, we introduce a distance between observables to quantify an accuracy of measurement. We derive an inequality that relates the achievable accuracy with noncommutativity between two observables. As a byproduct a necessary condition for two positive-operator-valued measures to be simultaneously measurable is obtained.