Solution to the mean king's problem with mutually unbiased bases for arbitrary levels
Solution to the mean king's problem with mutually unbiased bases for arbitrary levels
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DOI：
10.1103/physreva.73.050301
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发表时间：
2006-04
影响因子：
2.9
通讯作者：
G. Kimura;Hajime Tanaka;M. Ozawa
中科院分区：
文献类型：
--
作者：
G. Kimura;Hajime Tanaka;M. Ozawa
对于任意d级系统，重新考虑了互无偏基的平均王问题。Hayashi等人。Rev. A 71,052331(2005)]将问题与d-1相互正交拉丁方的极大集的存在性联系起来，在它们的限制设置中，只允许测量投影值测度。然而，当d=6或d=10时，我们无法找到问题的解。与他们的结果相反，我们表明，如果我们也允许正的算子值测度，对于任意水平，国王问题总是有一个解。在构造解时，我们使用组合设计理论中的正交阵列。
The mean king's problem with mutually unbiased bases is reconsidered for arbitrary d-level systems. Hayashi et al. [Phys. Rev. A 71, 052331 (2005)] related the problem to the existence of a maximal set of d-1 mutually orthogonal Latin squares, in their restricted setting that allows only measurements of projection-valued measures. However, we then cannot find a solution to the problem when, e.g., d=6 or d=10. In contrast to their result, we show that the king's problem always has a solution for arbitrary levels if we also allow positive operator-valued measures. In constructing the solution, we use orthogonal arrays in combinatorial design theory.