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
Solution to the mean king's problem with mutually unbiased bases for arbitrary levels. / Kimura, Gen; Tanaka, Hajime; Ozawa, Masanao.
In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 73, No. 5, 050301, 2006.Research output: Contribution to journal › Article
}
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 -