On bipartite unitary matrices generating subalgebra-preserving quantum operations

TL;DR

This paper characterizes bipartite unitary matrices that generate quantum operations preserving specific algebraic structures, revealing connections with quantum Latin squares and introducing a novel Sinkhorn-like algorithm.

Contribution

It provides a complete characterization of unitaries preserving diagonal, block-diagonal, and tensor product algebras, and links these to quantum Latin squares and a new generation algorithm.

Findings

Characterization of unitaries preserving certain algebras

Connections established with quantum Latin squares

Introduction of a Sinkhorn-like algorithm for quantum Latin squares

Abstract

We study the structure of bipartite unitary operators which generate via the Stinespring dilation theorem, quantum operations preserving some given matrix algebra, independently of the ancilla state. We characterize completely the unitary operators preserving diagonal, block-diagonal, and tensor product algebras. Some unexpected connections with the theory of quantum Latin squares are explored, and we introduce and study a Sinkhorn-like algorithm used to randomly generate quantum Latin squares.