An application of positive definite functions to the problem of MUBs

An application of positive definite functions to the problem of MUBs

We present a new approach to the problem of mutually unbiased bases (MUBs), based on positive definite functions on the unitary group. The method provides a new proof of the fact that there are at most d+1 MUBs in \mathbb{C}^d, and it may also lead to a proof of non-existence of complete systems of...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2018-03, Vol.146 (3), p.1143-1150
Hauptverfasser: KOLOUNTZAKIS, MIHAIL N., MATOLCSI, MÁTÉ, WEINER, MIHÁLY
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Sprache:eng
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Zusammenfassung:We present a new approach to the problem of mutually unbiased bases (MUBs), based on positive definite functions on the unitary group. The method provides a new proof of the fact that there are at most d+1 MUBs in \mathbb{C}^d, and it may also lead to a proof of non-existence of complete systems of MUBs in dimension 6 via a conjectured algebraic identity.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/13829