The analysis of formation of chaotic quantum states for two (or four) orthogonally polarized modes in a tunnelly-coupled optical fiber (TCOF) has been carried out. A special attention is devoted both to the structure of arising polarization instabilities and to the possibility to control of such a quantum state by procedure of quantum nondemolition measurements. New effect of polarization switching is obtained. A new method of generating correlated fluctuations in optical field, based on Raman-Nath diffraction by a fine grating, is discussed. A nonclassical effect is predicted: a suppression of quantum fluctuations below the level of full coherence in the sum of difference photon numbers for the transmitted and scattered waves. The physics of this phenomenon involves a correlation of quantum fluctuations in the intensities of two modes that are coupled nonlinearly. This correlation is most effective in the limit of parametric interaction between the waves in the medium.