  Noise correlations, such as those observable in the time of flight images of
a released cloud, are calculated for hard-core bosonic (HCB) atoms. We find
that the standard mapping of HCB systems onto spin-1/2 XY models fails in
application to computation of noise correlations due to the contribution of
multiply occupied virtual states in HCB systems. Such states do not exist in
spin models. An interesting manifestation of such states is the breaking of
particle-hole symmetry in HCB. We use noise correlations to explore quantum
coherence of strongly correlated bosons in the fermionized regime with and
without external parabolic confinement. Our analysis points to distinctive new
experimental signatures of the Mott phase.
