All Mutually Unbiased Bases in Dimensions Two to Five

Details All Mutually Unbiased Bases in Dimensions Two to Five All Mutually Unbiased Bases in Dimensions Two to Five

2009-07-23

arxiv.org/abs/0907.4097v2

Quantum Info. & Comp. Vol 10, pages 0803-0820, 2010

Physics

Mathematical Physics

As the published version with minor changes

Scientific paper

All complex Hadamard matrices in dimensions two to five are known. We use this fact to derive all inequivalent sets of mutually unbiased (MU) bases in low dimensions. We find a three-parameter family of triples of MU bases in dimension four and two inequivalent classes of MU triples in dimension five. We confirm that the complete sets of (d+1) MU bases are unique (up to equivalence) in dimensions below six, using only elementary arguments for d less than five.

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