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We examine the properties and behavior of the original Einstein-Podolsky-Rosen ͑EPR͒ wave function ͓Phys. Rev. 47, 777 ͑1935͔͒ and related Gaussian-correlated wave functions. We assess the degree of entanglement of these wave functions and consider an argument of Bell ͓Ann. ͑N.Y.͒ Acad. Sci. 480, 263 ͑1986͔͒ based on the Wigner phase-space distribution ͓Phys. Rev. 40, 749 ͑1932͔͒, which implies that the original EPR correlations can accommodate a local hidden-variable description. We extend Bell's analysis to the related Gaussian wave functions. We then show that it is possible to identify definite nonlocal aspects for the original EPR state and related states. We describe possible experiments that would demonstrate these nonlocal features through violations of Bell inequalities. The implications of our results, and in particular their relevance for the causal interpretation of quantum mechanics, are considered.

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There is an ongoing effort to quantify entanglement of quantum pure states for systems with more than two subsystems. We consider three approaches to this problem for three-qubit states: choosing a basis which puts the state into a standard form, enumerating ``local invariants,'' and using operational quantities such as the number of maximally entangled states which can be distilled. In this paper we evaluate a particular standard form, the {\it Schmidt form}, which is a generalization of the Schmidt decomposition for bipartite pure states. We show how the coefficients in this case can be parametrized in terms of five physically meaningful local invariants; we use this form to prove the efficacy of a particular distillation technique for GHZ triplets; and we relate the yield of GHZs to classes of states with unusual entanglement properties, showing that these states represent extremes of distillability as functions of two local invariants.Comment: 17 pages RevTeX 3.0 including 2 figures (encapsulated Postscript) Final version, to appear in Physics Letters

Methods for distilling Greenberger-Horne-Zeilinger (GHZ) states from arbitrary entangled tripartite pure states are described. These techniques work for virtually any input state. Each technique has two stages which we call primary and secondary distillations. Primary distillation produces a GHZ state with some probability, so that when applied to an ensemble of systems a certain percentage is discarded. Secondary distillation produces further GHZs from the discarded systems. These protocols are developed with the help of an approach to quantum information theory based on absolutely selective information, which has other potential applications.