Separation of unistochastic matrices from the double stochastic ones. Recovery of a 3 x 3 unitary matrix from experimental data

Abstract

The aim of the paper is to provide a constructive method for recovering a unitary matrix from experimental data. Since there is a natural immersion of unitary matrices within the set of double stochastic ones, the problem to solve is to find necessary and sufficient criteria that separate the two sets. A complete solution is provided for the 3-dimensional case, accompanied by a ${\chi }^2$ test necessary for the reconstruction of a unitary matrix from error affected data.

Comments: 28 pages