Mutually Unbiased Bases are Complex Projective 2-Designs

Details Mutually Unbiased Bases are Complex Projective 2-Designs Mutually Unbiased Bases are Complex Projective 2-Designs

2005-02-04

arxiv.org/abs/quant-ph/0502031v2

Physics

Quantum Physics

5 pages; minor corrections, two remarks on previous work added, submitted to 2005 IEEE International Symposium on Information

Scientific paper

Mutually unbiased bases (MUBs) are a primitive used in quantum information processing to capture the principle of complementarity. While constructions of maximal sets of d+1 such bases are known for systems of prime power dimension d, it is unknown whether this bound can be achieved for any non-prime power dimension. In this paper we demonstrate that maximal sets of MUBs come with a rich combinatorial structure by showing that they actually are the same objects as the complex projective 2-designs with angle set {0,1/d}. We also give a new and simple proof that symmetric informationally complete POVMs are complex projective 2-designs with angle set {1/(d+1)}.

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