Somshubhro Bandyopadhyay, P. Oscar Boykin, Vwani Roychowdhury, Farrokh Vatan
Published 2001-03-29, updated 2001-09-07Version 3
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.
Comments: Revised version. To appear in the special issue of Algorithmica on Quantum Algorithms and Quantum Cryptography
Mutually Unbiased Bases and Orthogonal Decompositions of Lie Algebras
Multipartite correlations in mutually unbiased bases
Product states and Schmidt rank of mutually unbiased bases in dimension six
