Solution to the mean king's problem with mutually unbiased bases for arbitrary levels

被引：22

作者：

Kimura, Gen ^{[1
]}

Tanaka, Hajime ^{[1
]}

Ozawa, Masanao ^{[1
]}

机构：

[1] Tohoku Univ, Grad Sch Informat Sci, Aoba Ku, Sendai, Miyagi 9808579, Japan

来源：

PHYSICAL REVIEW A | 2006年 / 73卷 / 05期

关键词：

Electronic structure;

D O I：

10.1103/PhysRevA.73.050301

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

The mean king's problem with mutually unbiased bases is reconsidered for arbitrary d-level systems. Hayashi [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.

引用

页数：4

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