Conditional density matrix: subsystems in quantum communication

A new quantum mechanical notion - Conditional Density Matrix - proposed by the authors, is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of quantum systems into subsystems and reunifications of subsystems into new joint systems. Conditional Density Matrix assigns a quantum state to a subsystem of a composite system under condition that another part of the composition system is in some pure state. It is shown that conditional density matrix naturally arises by expanding of reduced density matrix.