A mapping from the unitary to doubly stochastic matrices and symbols on a finite set

Details A mapping from the unitary to doubly stochastic matrices and symbols on a finite set A mapping from the unitary to doubly stochastic matrices and symbols on a finite set

2008-06-14

arxiv.org/abs/0806.2357v1

Mathematics

Quantum Algebra

13 pages

Scientific paper

10.1063/1.3043870

We prove that the mapping from the unitary to the doubly stochastic matrices
that maps a unitary matrix (u_{kl}) to the doubly stochastic matrix
(|u_{kl}|^2) is a submersion for almost all unitary matrices. The proof uses
the framework of operator symbols on a finite set. We give detailed proofs of
the results announced in our earlier preprint.

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