 Open quantum system

An open quantum system interacts with degrees of freedom treated as an environment. If system and environment jointly have density matrix ${\rho }_{SE}$, the system state is the partial trace ${\rho }_S={\mathrm{Tr}}_E{\rho }_{SE}$. Even unitary joint evolution can change the system's purity because correlations with the environment are discarded.

For example, an interaction mapping $|0⟩|e⟩$ to $|0⟩|e_0⟩$ and $|1⟩|e⟩$ to $|1⟩|e_1⟩$ multiplies the system coherence by $⟨e_1|e_0⟩$. Distinguishable environment states suppress that coherence. A time-local memoryless master equation is an additional approximation, not part of the definition of an open system.