Conditional Density Matrix: Systems and Subsystems in Quantum Mechanics
  A new quantum mechanical notion -- Conditional Density Matrix -- 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 composite system is in some pure state. 
V.V.Belokurov, O.A.Khrustalev, V.A.Sadovnichy, O.D.Timofeevskaya