Entanglement and products

Abstract

We consider a sequence of quantum states, ${\rho }_N$, associated with a submanifold $\Lambda$ of product of two integral compact Kähler manifolds. We show that, when $\Lambda$ is a product submanifold, then, in the semiclassical limit, these states are not entangled. We discuss whether geometry of $\Lambda$ (specifically $\Lambda$ being a product submanifold) has any relationship with entanglement properties of ${\rho }_N$.

arXiv commentTo appear in Linear and Multilinear Algebra