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.

28 pages

References in corpus (7)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• A New Approach to a Global Fit of the CKM Matrix
• Birkhoff's polytope and unistochastic matrices, N=3 and N=4
• A recursive parameterisation of unitary matrices
• Coherent States For SU(3)
• Global fits to the Cabibbo-Kobayashi-Maskawa matrix: unitarity condition method versus standard unitarity triangles approach

Cited by in corpus (7)

• Volume of the set of unistochastic matrices of order 3 and the mean Jarlskog invariant
• Hadamard Matrices from Mutually Unbiased Bases
• Absolute separability witnesses for symmetric multiqubit states
• Algebraic and geometric structures inside the Birkhoff polytope
• Cyclic measurements and simplified quantum state tomography
• CP nonconservation in the leptonic sector
• Robust Hadamard matrices, unistochastic rays in Birkhoff polytope and equi-entangled bases in composite spaces