Quantum Non-locality and Partial Transposition for Continuous-Variable Systems

TL;DR

This paper demonstrates that continuous-variable quantum states violating a Bell inequality must have negative partial transposition, linking nonlocality and bound entanglement in such systems.

Contribution

It establishes the first connection between nonlocality and bound entanglement for continuous-variable quantum systems.

Findings

Violating the Bell inequality implies negative partial transposition.

First link between nonlocality and bound entanglement in continuous variables.

Provides theoretical foundation for understanding entanglement properties.

Abstract

A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced in [Cavalcanti \emph{et al.}, Phys. Rev. Lett. {\bf 99}, 210405 (2007)]. We prove that any $n$-mode quantum state violating this inequality with quadrature measurements necessarily has a negative partial transposition. Our results thus establish the first link between nonlocality and bound entanglement for continuous-variable systems.