Maximal sets of mutually unbiased quantum states in dimension six

Steve Brierley, Stefan Weigert

Research output: Contribution to journalArticle (Academic Journal)peer-review

64 Citations (Scopus)


We study sets of pure states in a Hilbert space of dimension d which are mutually unbiased (MU), that is, the moduli of their scalar products are equal to zero, one, or 1∕√d. Each of these sets will be called a MU constellation, and if four MU bases were to exist for d=6, they would give rise to 35 different MU constellations. Using a numerical minimization procedure, we are able to identify only 18 of them in spite of extensive searches. The missing MU constellations provide the strongest numerical evidence so far that no seven MU bases exist in dimension 6.

Original languageEnglish
Article number042312
Number of pages8
JournalPhysical Review A: Atomic, Molecular and Optical Physics
Issue number4
Publication statusPublished - 11 Oct 2008

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