  We investigate the reduced dimensionality of highly anisotropic Bose-Einstein
condensates (BECs) in connection to the entanglement between its spatial
degrees of freedom. We argue that the reduced-dimensionality of the BEC is
physically meaningful in a regime where spatial correlations are negligible. We
handle the problem analytically within the mean-field approximation for general
quasi-one-dimensional and -two-dimensional geometries, and obtain the optimal
reduced-dimension, pure-state description of the condensate mean field. We give
explicit solutions to the case of harmonic potentials, which we compare against
exact numerical integration of the three-dimensional Gross-Pitaevskii equation.
