Von Neumann entropy and the replica method.
The calculation of the von Neumann entropy can be proven a tough problem, since it involves the diagonalization of very large, even infinite-dimensional, density matrices. However, one can overcome this difficulty with the help of replica method, a tool which is used in statistical physics and quantum field theory. We have applied the method in the field of quantum optics, where it enabled access to the entropic characteristics of the Bogoliubov transformation effected by a two-mode squeezer or optical amplifier, and we have studied the Bose-Einstein condensation phenomenon in terms of the quantum information quantity of mutual information.