All Mutually Unbiased Bases in Dimensions Two to Five
Stephen Brierley, Stefan Weigert, Ingemar Bengtsson
TL;DR
This paper classifies all mutually unbiased bases in dimensions two to five, revealing a complete understanding of their structures and confirming their uniqueness in low dimensions.
Contribution
It derives all inequivalent MU bases in low dimensions and identifies new parameterized families and classes, advancing the classification of quantum measurement bases.
Findings
Complete sets of MU bases are unique in dimensions below six.
Discovered a three-parameter family of MU bases in dimension four.
Identified two inequivalent classes of MU triples in dimension five.
Abstract
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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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Finite Group Theory Research