The Birkhoff theorem for unitary matrices of prime dimension

Abstract

The Birkhoff's theorem states that any doubly stochastic matrix lies inside a convex polytope with the permutation matrices at the corners. It can be proven that a similar theorem holds for unitary matrices with equal line sums for prime dimensions.

References in corpus (2)

• Sinkhorn normal form for unitary matrices
• Decomposition of bipartite and multipartite unitary gates into the product of controlled unitary gates

Cited by in corpus (3)

• A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps
• The Birkhoff theorem for unitary matrices of arbitrary dimensions
• The decomposition of an arbitrary $2^w\times 2^w$ unitary matrix into signed permutation matrices