International Journal of Modern Physics B Vol. 19, No. 26 (2005) 3897–3921 c  World Scientific Publishing Company TRANSLATIONAL ENTANGLEMENT AND TELEPORTATION OF MATTER WAVEPACKETS BY COLLISIONS AND HALF-COLLISIONS L. FISCH, A. TAL and G. KURIZKI Dept. of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel Received 9 September 2005 To date, the translationally-entangled state originally proposed by Einstein, Podolsky and Rosen (EPR) in 1935 has not been experimentally realized for massive particles. Opatrn´ y and Kurizki [Phys. Rev. Lett. 86, 3180 (2000)] have suggested the creation of a position- and momentum-correlated, i.e., translationally-entangled, pair of par- ticles approximating the EPR state by dissociation of cold diatomic molecules, and further manipulation of the EPR pair effecting matter-wave teleportation. Here we aim at setting the principles of and quantifying translational entanglement by collisions and half-collisions. In collisions, the resonance width s and the initial phase-space distribu- tions are shown to determine the degree of post-collisional momentum entanglement. Half-collisions (dissociation) are shown to yield different types of approximate EPR states. We analyse a feasible realization of translational EPR entanglement and telepor- tation via cold-molecule Raman dissociation and subsequent collisions, resolving both practical and conceptual difficulties it has faced so far: How to avoid entanglement loss due to the wavepacket spreading of the dissociation fragments? How to measure both position and momentum correlations of the dissociation fragments with sufficient ac- curacy to verify their EPR correlations? How to reliably perform two-particle (Bell) position and momentum measurements on one of the fragments and the wavepacket to be teleported? Keywords : Entanglement; quantum information; continuous variables; quantum telepor- tation; molecular dynamics; cold-atom collisions. PACS numbers: 03.67.Hk, 03.65.Ud, 39.20.+q 1. Introduction Einstein, Podolsky and Rosen (EPR) suggested the EPR state of two particles with well-defined momentum-sum and position-difference 1 in order to illustrate their dissatisfaction with what they interpreted as the lack of completeness of quan- tum mechanics. Schr¨ oedinger later identified the “paradoxical” features of such a state with two-particle entanglement involving continuous variables. 2 Despite the fact that entanglement and EPR-like correlations have become key notions in contemporary physics, the original EPR scenario 1 has been studied only to a limited 3897