All Mutually Unbiased Product Bases in Dimension Six

Details All Mutually Unbiased Product Bases in Dimension Six All Mutually Unbiased Product Bases in Dimension Six

2011-11-15

arxiv.org/abs/1111.3632v2

J. Phys. A: Math. Theor. 45 (2012) 135307

Physics

Quantum Physics

32 pages, 3 figures, identical to published version

Scientific paper

10.1088/1751-8113/45/13/13530

All mutually unbiased bases in dimension six consisting of product states only are constructed. Several continuous families of pairs and two triples of mutually unbiased product bases are found to exist but no quadruple. The exhaustive classification leads to a proof that a complete set of seven mutually unbiased bases, if it exists, cannot contain a triple of mutually unbiased product bases.

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