We perform first-principles quantum simulations of dissociation of trapped, spatially inhomogeneous Bose-Einstein condensates of molecular dimers. Specifically, we study spatial pair correlations of atoms produced in dissociation after time of flight. We find that the observable correlations may significantly degrade in systems with spatial inhomogeneity compared to the predictions of idealized uniform models. We show how binning of the signal can enhance the detectable correlations and lead to the violation of the classical Cauchy-Schwartz inequality and relative number squeezing. DOI: 10.1103/PhysRevLett.99.220404 PACS numbers: 03.75.Nt, 03.65.Ud, 03.75.Gg Producing and utilizing quantum mechanical correlations between entangled particle pairs are major themes in quantum mechanics research. In this Letter we investigate correlations of the kind used by Einstein, Podolsky, and Rosen (EPR) to argue that local realism is inconsistent with quantum mechanics being a complete theory of nature [1]. EPR type nonlocal correlations were first produced experimentally in the form of photon pairs from nondegenerate parametric down-conversion [2]. Here, the correlations are observed between the optical quadrature amplitudes of spatially separated signal and idler beams, which are analogous to canonical position and momentum variables originally discussed by EPR.It should be possible to extend this type of experiment to ultracold atoms, which would allow the investigation of EPR correlations for particles with nonzero rest mass. These might be produced by the transfer of correlations from photons to atoms [3], or else by nonlinear matterwave interactions. The latter include atomic four-wave mixing via Bose-Einstein condensate (BEC) collisions [4,5] and matter-wave down-conversion via dissociation of a molecular BEC [6 -9]. Although the direct measurement of matter-wave quadrature correlations of this type is a challenging task [9], a simpler measurement of densitydensity correlations -as a prerequisite for the EPR quadrature correlations -can be performed with current experimental techniques.In this Letter we perform first-principles quantum simulations of dissociation of a BEC of molecular dimers into pair-correlated bosonic atoms. This has been demonstrated experimentally using ultracold (but not Bose condensed) 87 Rb 2 dimers [10], although the atom correlations have not yet been measured. In the case of fermionic atoms [11,12], such as in dissociation of 40 K 2 dimers [13], the densitydensity correlations between the atoms in two different spin states have been measured; this case, however, currently resists first-principles quantum simulations. Nevertheless, many insights from the present bosonic case also apply to the fermionic case, and to correlations produced via BEC four-wave mixing [14]. For example, the importance of operationally well defined measures of correlations, the role of spatial inhomogeneity, and the trade-off between image resolution and binning to enhance correlation detection.Measurements now ch...