  Quantum photon-number fluctuation and correlation of bound soliton pairs in
mode-locked fiber lasers are studied based on the complex Ginzburg-Landau
equation model. We find that, depending on their phase difference, the total
photon-number noise of the bound soliton pair can be larger or smaller than
that of a single soliton and the two solitons in the soliton pairs are with
positive or negative photon-number correlation, correspondingly. It is
predicted for the first time that out-of-phase soliton pairs can exhibit less
noises due to negative correlation.
