Kinetic equations for quantum information

We study several kinetic equations for quantum information density (QID) based on the classical dynamical statistical information theory (Trans. Beijing Inst. Technol. 24 (2004) 1; Acta Phys. Scinica 53 (2004) 2852). We find that the Liouville equation, SKE and quantum Fokker–Planck equation for information density or entropy operator share the same formalisms as that of density operator. This allows one to apply QID directly to perform quantum information. Furthermore, we also obtain a quantum Fokker–Planck equation for information density which exposes that flow of shift and diffusion for information density introduce change of total derivative of information density with respect to time. As an application, the complex spectrum of SKE for information density has been discussed, which can be used to study stability of quantum computing in a spin-boson model.