Dynamical Equations for Quantum Information and Application in Information Channel

We establish several dynamical equations for quantum information density. It is demonstrated that quantum information density shares the same formalism of the Liouville equation, subdynamics kinetic equation and Fokker-Planck equation as the density operator and also possesses the superposition property. These allow one to use quantum information density directly to model quantum information. The kinetic equations for quantum information density reveal that the dynamical process of quantum information may be related to dissipative, Markovian, or diffusional information flows, together causing irreversibility. Finally, we discuss superposition of quantum information density, which allows us to construct a quantum information channel in the coherent state representation using harmonic oscillator based encoded quantum information, and obtain a formula for quantum dynamical mutual information.