  We investigate numerically the momentum correlations in a two dimensional,
harmonically trapped interacting Bose system at $T=0$ temperature, by using a
particle number preserving Bogoliubov approximation. Interaction induced
quantum fluctuations of the quasi-condensate lead to a large anti-correlation
dip between particles of wave numbers $\mathbf{k}$ and $-\mathbf{k}$ for
$|\mathbf{k}|\sim 1/R_c$, with $R_c$ typical size of the condensate. The
anti-correlation dip found is a clear fingerprint of coherent quantum
fluctuations of the condensate. In contrast, for larger wave numbers,
$|\mathbf{k}| >> 1/R_c$, a weak positive correlation is found between particles
of wave numbers $\mathbf{k}$ and $-\mathbf{k}$, in accordance with the
Bogoliubov result for homogeneous interacting systems.
