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

Journal Article · Mon May 15 00:00:00 EDT 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.73.0· OSTI ID:20787188

Kimura, Gen; Tanaka, Hajime; Ozawa, Masanao ^[1]

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1. Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579 (Japan)

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.

• OSTI ID: 20787188
• Journal Information: Physical Review. A, Vol. 73, Issue 5; Other Information: DOI: 10.1103/PhysRevA.73.050301; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

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