All mutually unbiased bases in dimensions two to five

Authors:
Stephen Brierley;Stefan Weigert;Ingemar Bengtsson
Affiliations:
Department of Mathematics, University of York, York, UK;Department of Mathematics, University of York, York, UK;Fysikum, Stockholms Universitet, Stockholm, Sweden
Venue:
Quantum Information & Computation
Year:
2010

Citing 2
Cited 3

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Abstract

All complex Hadamard matrices in dimensions two to five are known. We use this fact toderive all inequivalent sets of mutually unbiased (MU) bases in low dimensions. We finda three-parameter family of triples of MU bases in dimension four and two inequivalentclasses 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 elementaryarguments for d less than five.