Maximal Sets of Mutually Unbiased Quantum States in Dimension Six

Details Maximal Sets of Mutually Unbiased Quantum States in Dimension Six Maximal Sets of Mutually Unbiased Quantum States in Dimension Six

2008-08-12

arxiv.org/abs/0808.1614v1

Phys. Rev. A 78, 042312 (2008)

Physics

Quantum Physics

19 pages, 6 figures, 4 tables

Scientific paper

10.1103/PhysRevA.78.042312

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.

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