Verifying continuous-variable entanglement in finite spaces

TL;DR

This paper presents a method to verify entanglement in bipartite and multipartite quantum states by reducing the problem to finite-dimensional subspaces, demonstrating that entanglement is fundamentally a finite-dimensional property.

Contribution

It introduces a general approach to verify entanglement in infinite-dimensional Hilbert spaces by focusing on finite-dimensional subspaces, extending to multipartite states.

Findings

Entanglement verification can be reduced to finite-dimensional subspaces.

Entanglement is a finite-dimensional property.

Applicable to both bipartite and multipartite quantum states.

Abstract

Starting from arbitrary Hilbert spaces, we reduce the problem to verify entanglement of any bipartite quantum state to finite dimensional subspaces. Hence, entanglement is a finite dimensional property. A generalization for multipartite quantum states is also given.