dorsal/arxiv
View SchemaA new proof for the existence of mutually unbiased bases
| Authors | Somshubhro Bandyopadhyay, P. Oscar Boykin, Vwani Roychowdhury, Farrokh Vatan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103162 |
| URL | https://arxiv.org/abs/quant-ph/0103162 |
Abstract
We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions which are power of a prime is presented. It is also proved that in any dimension d the number of mutually unbiased bases is at most d+1. An explicit representation of mutually unbiased observables in terms of Pauli matrices are provided for d=2^m.
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"abstract": "We develop a strong connection between maximally commuting bases of\northogonal unitary matrices and mutually unbiased bases. A necessary condition\nof the existence of mutually unbiased bases for any finite dimension is\nobtained. Then a constructive proof of the existence of mutually unbiased bases\nfor dimensions which are power of a prime is presented. It is also proved that\nin any dimension d the number of mutually unbiased bases is at most d+1. An\nexplicit representation of mutually unbiased observables in terms of Pauli\nmatrices are provided for d=2^m.",
"arxiv_id": "quant-ph/0103162",
"authors": [
"Somshubhro Bandyopadhyay",
"P. Oscar Boykin",
"Vwani Roychowdhury",
"Farrokh Vatan"
],
"categories": [
"quant-ph"
],
"title": "A new proof for the existence of mutually unbiased bases",
"url": "https://arxiv.org/abs/quant-ph/0103162"
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