Constructions of Mutually Unbiased Bases

Details Constructions of Mutually Unbiased Bases Constructions of Mutually Unbiased Bases

2003-09-15

arxiv.org/abs/quant-ph/0309120v1

Physics

Quantum Physics

8 pages latex

Scientific paper

Two orthonormal bases B and B' of a d-dimensional complex inner-product space are called mutually unbiased if and only if ||^2=1/d holds for all b in B and b' in B'. The size of any set containing (pairwise) mutually unbiased bases of C^d cannot exceed d+1. If d is a power of a prime, then extremal sets containing d+1 mutually unbiased bases are known to exist. We give a simplified proof of this fact based on the estimation of exponential sums. We discuss conjectures and open problems concerning the maximal number of mutually unbiased bases for arbitrary dimensions.

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