dorsal/arxiv
View SchemaConstructions of Mutually Unbiased Bases
| Authors | Andreas Klappenecker, Martin Roetteler |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0309120 |
| URL | https://arxiv.org/abs/quant-ph/0309120 |
| Journal | Proceedings of the 7th International Conference on Finite Fields (Fq7), Toulouse, France, Springer LNCS, pp. 137-144, 2004 |
Abstract
Two orthonormal bases B and B' of a d-dimensional complex inner-product space are called mutually unbiased if and only if |<b|b'>|^2=1/d holds for all b in B and b' in B'. The size of any set containing (pairwise) mutually unbiased bases of C^d cannot exceed d+1. If d is a power of a prime, then extremal sets containing d+1 mutually unbiased bases are known to exist. We give a simplified proof of this fact based on the estimation of exponential sums. We discuss conjectures and open problems concerning the maximal number of mutually unbiased bases for arbitrary dimensions.
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"abstract": "Two orthonormal bases B and B\u0027 of a d-dimensional complex inner-product space\nare called mutually unbiased if and only if |\u003cb|b\u0027\u003e|^2=1/d holds for all b in B\nand b\u0027 in B\u0027. The size of any set containing (pairwise) mutually unbiased bases\nof C^d cannot exceed d+1. If d is a power of a prime, then extremal sets\ncontaining d+1 mutually unbiased bases are known to exist. We give a simplified\nproof of this fact based on the estimation of exponential sums. We discuss\nconjectures and open problems concerning the maximal number of mutually\nunbiased bases for arbitrary dimensions.",
"arxiv_id": "quant-ph/0309120",
"authors": [
"Andreas Klappenecker",
"Martin Roetteler"
],
"categories": [
"quant-ph",
"cs.ET"
],
"journal_ref": "Proceedings of the 7th International Conference on Finite Fields\n (Fq7), Toulouse, France, Springer LNCS, pp. 137-144, 2004",
"title": "Constructions of Mutually Unbiased Bases",
"url": "https://arxiv.org/abs/quant-ph/0309120"
},
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