Solution to the mean king's problem with mutually unbiased bases for arbitrary levels
- 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, Journal Name: Physical Review. A Journal Issue: 5 Vol. 73; ISSN 1050-2947; ISSN PLRAAN
- Country of Publication:
- United States
- Language:
- English
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