On orthostochastic, unistochastic and qustochastic matrices

DOI10.1016/j.laa.2007.09.022zbMath1139.15010arXiv0708.4051OpenAlexW2037192928MaRDI QIDQ2469544

Oleg Chterental, Dragomir Ž. Djoković

Publication date: 6 February 2008

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.4051

zbMATH Keywords

singular pointsHadamard matricescritical pointsquaternionssymplectic matricesunitary matricesdoubly stochastic matricesorthogonal matricesmutually unbiased basesorthostochastic matricesunistochastic matricesclassical compact groupsqustochastic matricessplitting matrices

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Quantum computation (81P68) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Stochastic matrices (15B51)

Related Items (11)

Unistochastic Matrices and Related Problems ⋮ On a multi-dimensional generalization of the notions of orthostochastic and unistochastic matrices ⋮ On 6× 6 complex Hadamard matrices containing two nonintersecting identical 3× 3 submatrices ⋮ Entropy of orthogonal matrices and minimum distance orthostochastic matrices from the uniform van der Waerden matrices ⋮ The 4 × 4 Orthostochastic Variety ⋮ Block-circulant complex Hadamard matrices ⋮ Maximal energy extraction via quantum measurement ⋮ Definite determinantal representations via orthostochastic matrices ⋮ Optimization problems with orthogonal matrix constraints ⋮ On some p-almost Hadamard matrices ⋮ Coordinate-wise powers of algebraic varieties

Uses Software

• Maple

Cites Work

• Unnamed Item
• \(3\times 3\) orthostochastic matrices and the convexity of generalized numerical ranges
• Permutation matrices whose convex combinations are orthostochastic
• Defect of a unitary matrix
• Set of \(3\times 3\) orthostochastic matrices
• A new proof for the existence of mutually unbiased bases
• Birkhoff's polytope and unistochastic matrices, \(N=3\) and \(N=4\)
• A Concise Guide to Complex Hadamard Matrices
• Separation of unistochastic matrices from the double stochastic ones: Recovery of a 3×3 unitary matrix from experimental data
• Mutually unbiased bases and Hadamard matrices of order six
• Entropy and Hadamard matrices

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