On bipartite unitary matrices generating subalgebra-preserving quantum operations

Tristan Benoist (1, 2) , Ion Nechita (2, 1)

1 ICQ - Cohérence Quantique (LPT)
2 LPT - Laboratoire de Physique Théorique

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.

Domaines: Physique mathématique [math-ph]; Algèbres quantiques [math.QA]; Physique Quantique [quant-ph]

Tristan Benoist, Ion Nechita. On bipartite unitary matrices generating subalgebra-preserving quantum operations. Linear Algebra and its Applications, 2017, 521, pp.70-103. ⟨10.1016/j.laa.2017.01.020⟩. ⟨hal-01381093⟩