On the Impossibility to Extend Triples of Mutually Unbiased Product Bases in Dimension Six

Abstract

An analytic proof is given which shows that it is impossible to extend any triple of mutually unbiased (MU) product bases in dimension six by a single MU vector. Furthermore, the 16 states obtained by removing two orthogonal states from any MU product triple cannot figure in a (hypothetical) complete set of seven MU bases. These results follow from exploiting the structure of MU product bases in a novel fashion, and they are among the strongest ones obtained for MU bases in dimension six without recourse to computer algebra.

12 pages, identical to published version

References in corpus (3)

• Maximal Sets of Mutually Unbiased Quantum States in Dimension Six
• Numerical evidence for the maximum number of mutually unbiased bases in dimension six
• Variations on a theme of Heisenberg, Pauli and Weyl

Cited by in corpus (6)

• Mutually unbiased triplets from non-affine families of complex Hadamard matrices in dimension six
• States that "look the same" with respect to every basis in a mutually unbiased set
• Real Entries of Complex Hadamard Matrices and Mutually Unbiased Bases in Dimension Six
• Constructions of mutually unbiased entangled bases
• $H_2$-reducible matrices in six-dimensional mutually unbiased bases
• Some special complex Hadamard matrices of order six