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A correlated many-body calculation is presented to characterize the Shannoninformation entropy of trapped interacting bosons. We reformulate the one-bodyShannon information entropy in terms of the one-body probability density. Theminimum limit of the entropy uncertainty relation (EUR) is approached by making$N$ very small in our numerical work. We examine the effect of correlations inthe calculation of information entropy. Comparison with the mean-field resultshows that the correlated basis function is indeed required to characterize theimportant features of the information entropies. We also accurately calculatethe point of critical instability of an attractive BEC, which is in closeagreement with the experimental value. Next we calculate two-body entropies inposition and momentum spaces and study quantum correlations in the attractiveBEC.

Correlated many-body calculation to study characteristics of Shannon information entropy for ultracold trapped interacting bosons