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

Gen Kimura, Hajime Tanaka, Masanao Ozawa

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19 Citations (Scopus)


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.

Original languageEnglish
Article number050301
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number5
Publication statusPublished - 2006
Externally publishedYes


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Physics and Astronomy(all)

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