dorsal/arxiv
View SchemaSolution to the Mean King's problem with mutually unbiased bases for arbitrary levels
| Authors | Gen Kimura, Hajime Tanaka, Masanao Ozawa |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604096 |
| URL | https://arxiv.org/abs/quant-ph/0604096 |
| DOI | 10.1103/PhysRevA.73.050301 |
| Journal | Phys. Rev. A 73, 050301(R) (2006). |
Abstract
The Mean King's problem with mutually unbiased bases is reconsidered for arbitrary d-level systems. Hayashi, Horibe and Hashimoto [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.
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"abstract": "The Mean King\u0027s problem with mutually unbiased bases is reconsidered for\narbitrary d-level systems. Hayashi, Horibe and Hashimoto [Phys. Rev. A 71,\n052331 (2005)] related the problem to the existence of a maximal set of d-1\nmutually orthogonal Latin squares, in their restricted setting that allows only\nmeasurements of projection-valued measures. However, we then cannot find a\nsolution to the problem when e.g., d=6 or d=10. In contrast to their result, we\nshow that the King\u0027s problem always has a solution for arbitrary levels if we\nalso allow positive operator-valued measures. In constructing the solution, we\nuse orthogonal arrays in combinatorial design theory.",
"arxiv_id": "quant-ph/0604096",
"authors": [
"Gen Kimura",
"Hajime Tanaka",
"Masanao Ozawa"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.050301",
"journal_ref": "Phys. Rev. A 73, 050301(R) (2006).",
"title": "Solution to the Mean King\u0027s problem with mutually unbiased bases for arbitrary levels",
"url": "https://arxiv.org/abs/quant-ph/0604096"
},
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