Greenberger-Horne-Zeilinger nonlocality for continuous variable systems

As a development of our previous work, this paper is concerned with the Greenberger-Horne-Zeilinger (GHZ) nonlocality for continuous variable cases. The discussion is based on the introduction of a pseudospin operator, which has the same algebra as the Pauli operator, for each of the $N$ modes of a light field. Then the Bell-CHSH (Clauser, Horne, Shimony and Holt) inequality is presented for the $N$ modes, each of which has a continuous degree of freedom. Following Mermin's argument, it is demonstrated that for $N$-mode parity-entangled GHZ states (in an infinite-dimensional Hilbert space) of the light field, the contradictions between quantum mechanics and local realism grow exponentially with $N$, similarly to the usual $N$-spin cases.Comment: RevTEX; comments are welcomed; new version with minor change

Einstein, incompleteness, and the epistemic view of quantum states

Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. Indeed, representatives of each class can be found among existing constructions for two-dimensional Hilbert spaces. Our approach also provides a fruitful new perspective on arguments for the nonlocality and incompleteness of quantum theory. Specifically, we show that for models wherein the quantum state has the status of something real, the failure of locality can be established through an argument considerably more straightforward than Bell's theorem. The historical significance of this result becomes evident when one recognizes that the same reasoning is present in Einstein's preferred argument for incompleteness, which dates back to 1935. This fact suggests that Einstein was seeking not just any completion of quantum theory, but one wherein quantum states are solely representative of our knowledge. Our hypothesis is supported by an analysis of Einstein's attempts to clarify his views on quantum theory and the circumstance of his otherwise puzzling abandonment of an even simpler argument for incompleteness from 1927.Comment: 18 pages, 8 figures, 1 recipe for cupcakes; comments welcom

Dynamics of entanglement between two trapped atoms

We investigate the dynamics of entanglement between two continuous variable quantum systems. The model system consists of two atoms in a harmonic trap which are interacting by a simplified s-wave scattering. We show, that the dynamically created entanglement changes in a steplike manner. Moreover, we introduce local operators which allow us to violate a Bell-CHSH inequality adapted to the continuous variable case. The correlations show nonclassical behavior and almost reach the maximal quantum mechanical value. This is interesting since the states prepared by this interaction are very different from any EPR-like state.Comment: 9 page