Solution to the Mean King's problem with mutually unbiased bases for arbitrary levels
量子物理
2009-11-13 v1
摘要
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.
引用
@article{arxiv.quant-ph/0604096,
title = {Solution to the Mean King's problem with mutually unbiased bases for arbitrary levels},
author = {Gen Kimura and Hajime Tanaka and Masanao Ozawa},
journal= {arXiv preprint arXiv:quant-ph/0604096},
year = {2009}
}
备注
REVTeX4, 4 pages