A new proof for the existence of mutually unbiased bases

2001/03/29 by Somshubhro Bandyopadhyay, P. Oscar Boykin, Bandyopadhyay, Somshubhro +5 · 8 citations
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0103162

Revised version. To appear in the special issue of Algorithmica on Quantum Algorithms and Quantum Cryptography

arxiv created 2001/09/07 · arxiv updated 2009/12/01

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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