On orthostochastic, unistochastic and qustochastic matrices

Details On orthostochastic, unistochastic and qustochastic matrices On orthostochastic, unistochastic and qustochastic matrices

2007-08-30

arxiv.org/abs/0708.4051v1

Linear Algebra and Its Applications 428 (2008), 1178-2001

Physics

Mathematical Physics

29 pages, no figures, 5 open problems

Scientific paper

We introduce qustochastic matrices as the bistochastic matrices arising from quaternionic unitary matrices by replacing each entry with the square of its norm. This is the quaternionic analogue of the unistochastic matrices studied by physicists. We also introduce quaternionic Hadamard matrices and quaternionic mutually unbiased bases (MUB). In particular we show that the number of MUB in an n-dimensional quaternionic Hilbert space is at most 2n+1. The bound is attained for n=2. We also determine all quaternionic Hadamard matrices of size at most 4.

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