Maximal Sets of Mutually Unbiased Quantum States in Dimension Six

Preprint

12 August 2008

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.0808.1614

Abstract

We study sets of pure states in a Hilbert space of dimension d which are mutually unbiased (MU), that is, the squares of the moduli of their scalar products are equal to zero, one, or 1/d. 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 minimisation 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 six.

Keywords

MUTUALLY UNBIASED
MU CONSTELLATIONS
UNBIASED QUANTUM
QUANTUM STATES
DIMENSION SIX
HILBERT SPACE
MAXIMAL SETS
MU BASES

All Related Versions

Version 1, 2008-08-12, ArXiv
Published version: Physical Review A, 78 (4), 042312.

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