A New Proof for the Existence of Mutually Unbiased Bases (2001)
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BibTeX
@MISC{Bandyopadhyay01anew,
author = {Somshubhro Bandyopadhyay and P. Oscar Boykin and Vwani Roychowdhury and Farrokh Vatan},
title = {A New Proof for the Existence of Mutually Unbiased Bases},
year = {2001}
}
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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 that are powers of primes 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 . 1
