Mutually Unbiased Bases and Semi-definite Programming

Abstract

A complex Hilbert space of dimension six supports at least three but not more than seven mutually unbiased bases. Two computer-aided analytical methods to tighten these bounds are reviewed, based on a discretization of parameter space and on Grobner bases. A third algorithmic approach is presented: the non-existence of more than three mutually unbiased bases in composite dimensions can be decided by a global optimization method known as semidefinite programming. The method is used to confirm that the spectral matrix cannot be part of a complete set of seven mutually unbiased bases in dimension six.

11 pages,

References in corpus (4)

• A complete family of separability criteria
• Maximal Sets of Mutually Unbiased Quantum States in Dimension Six
• Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions
• A Robust Semidefinite Programming Approach to the Separability Problem