TY - JOUR

T1 - Solution to the mean king's problem with mutually unbiased bases for arbitrary levels

AU - Kimura, Gen

AU - Tanaka, Hajime

AU - Ozawa, Masanao

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.73.050301

DO - 10.1103/PhysRevA.73.050301

M3 - Article

AN - SCOPUS:33646406835

VL - 73

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 5

M1 - 050301

ER -