Article

# Separability Properties of Three-mode Gaussian States

Physical Review A (Impact Factor: 3.04). 03/2001; DOI: 10.1103/PhysRevA.64.052303

Source: arXiv

- [Show abstract] [Hide abstract]

**ABSTRACT:**We investigate the genuine multipartite nonlocality of three-mode Gaussian states of continuous variable systems. For pure states, we present a simplified procedure to obtain the maximum violation of the Svetlichny inequality based on displaced parity measurements, and we analyze its interplay with genuine tripartite entanglement measured via Rényi-2 entropy. The maximum Svetlichny violation admits tight upper and lower bounds at fixed tripartite entanglement. For mixed states, no violation is possible when the purity falls below 0.86. We also explore a set of recently derived weaker inequalities for three-way nonlocality, finding violations for all tested pure states. Our results provide a strong signature for the nonclassical and nonlocal nature of Gaussian states despite their positive Wigner function, and lead to precise recipes for its experimental verification.Physical Review Letters 01/2014; 112(1):010401. · 7.73 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We review the physics of some hybrid optomechanical systems consisting of a mechanical oscillator interacting with both a radiation mode and an additional matter-like system. We concentrate on the cases embodied by either a single or a multi-atom system (a Bose-Einstein condensate, in particular) and discuss a wide range of physical effects, from passive mechanical cooling to the set-up of multipartite entanglement, from optomechanical non-locality to the achievement of non-classical states of a single mechanical mode. The reviewed material showcases the viability of hybridised cavity optomechanical systems as basic building blocks for quantum communication networks and quantum state-engineering devices, possibly empowered by the use of quantum and optimal control techniques. The results that we discuss are instrumental to the promotion of hybrid optomechanical devices as promising experimental platforms for the study of non-classicality at the genuine mesoscopic level.02/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**Starting with a set of conditions for bipartite separability of arbitrary quantum states in any dimension and expressed in terms of arbitrary operators whose commutator is a $c$-number, we derive a hierarchy of conditions for tripartite separability of continuous-variable three-mode quantum states. These conditions have the form of inequalities for higher-order moments of linear combinations of the mode operators. They enable one to distinguish between all possible kinds of tripartite separability, while the strongest violation of these inequalities is a sufficient condition for genuine tripartite entanglement. We construct Gaussian states for which the violation of our conditions grows exponentially with the order of the moments of the mode operators. By going beyond second moments, our conditions are expected to be useful as well for the detection of tripartite entanglement of non-Gaussian states.02/2014;

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.