dorsal/arxiv
View SchemaMutually Unbiased Bases are Complex Projective 2-Designs
| Authors | Andreas Klappenecker, Martin Roetteler |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502031 |
| URL | https://arxiv.org/abs/quant-ph/0502031 |
| Journal | Proceedings 2005 IEEE International Symposium on Information Theory (ISIT 2005), Adelaide, Australia, pp. 1740-1744, 2005 |
Abstract
Mutually unbiased bases (MUBs) are a primitive used in quantum information processing to capture the principle of complementarity. While constructions of maximal sets of d+1 such bases are known for systems of prime power dimension d, it is unknown whether this bound can be achieved for any non-prime power dimension. In this paper we demonstrate that maximal sets of MUBs come with a rich combinatorial structure by showing that they actually are the same objects as the complex projective 2-designs with angle set {0,1/d}. We also give a new and simple proof that symmetric informationally complete POVMs are complex projective 2-designs with angle set {1/(d+1)}.
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"abstract": "Mutually unbiased bases (MUBs) are a primitive used in quantum information\nprocessing to capture the principle of complementarity. While constructions of\nmaximal sets of d+1 such bases are known for systems of prime power dimension\nd, it is unknown whether this bound can be achieved for any non-prime power\ndimension. In this paper we demonstrate that maximal sets of MUBs come with a\nrich combinatorial structure by showing that they actually are the same objects\nas the complex projective 2-designs with angle set {0,1/d}. We also give a new\nand simple proof that symmetric informationally complete POVMs are complex\nprojective 2-designs with angle set {1/(d+1)}.",
"arxiv_id": "quant-ph/0502031",
"authors": [
"Andreas Klappenecker",
"Martin Roetteler"
],
"categories": [
"quant-ph",
"cs.ET"
],
"journal_ref": "Proceedings 2005 IEEE International Symposium on Information\n Theory (ISIT 2005), Adelaide, Australia, pp. 1740-1744, 2005",
"title": "Mutually Unbiased Bases are Complex Projective 2-Designs",
"url": "https://arxiv.org/abs/quant-ph/0502031"
},
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