Entanglement and products

TL;DR

This paper investigates the relationship between the geometric structure of certain quantum states associated with product submanifolds and their entanglement properties in the semiclassical limit, revealing that product structures lead to non-entangled states.

Contribution

It demonstrates that quantum states linked to product submanifolds are not entangled in the semiclassical limit, connecting geometric properties with quantum entanglement.

Findings

States associated with product submanifolds are not entangled semiclassically.

Geometry of the submanifold influences entanglement properties.

Discussion on the potential relationship between geometry and entanglement.

Abstract

We consider a sequence of quantum states, $\rho_N$, associated with a submanifold $\Lambda$ of product of two integral compact K\"ahler 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 $\rho_N$.