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