### Abstract

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 language | English |
---|---|

Article number | 050301 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 73 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2006 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*73*(5), [050301]. https://doi.org/10.1103/PhysRevA.73.050301

**Solution to the mean king's problem with mutually unbiased bases for arbitrary levels.** / Kimura, Gen; Tanaka, Hajime; Ozawa, Masanao.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 73, no. 5, 050301. https://doi.org/10.1103/PhysRevA.73.050301

}

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.

UR - http://www.scopus.com/inward/record.url?scp=33646406835&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646406835&partnerID=8YFLogxK

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 -