The Birkhoff theorem for unitary matrices of arbitrary dimensions

Abstract

It was shown recently that Birkhoff's theorem for doubly stochastic matrices can be extended to unitary matrices with equal line sums whenever the dimension of the matrices is prime. We prove a generalization of the Birkhoff theorem for unitary matrices with equal line sums for arbitrary dimension.

This manuscript presents a proof for the general unitary birkhoff theorem, conjectured in arXiv:1509.08626

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