= 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> $\rho_S=\operatorname{Tr}_E\rho_{SE}$. Even unitary joint evolution can change the system's <purity> because correlations with the environment are discarded.
For example, an interaction mapping $|0\rangle|e\rangle$ to $|0\rangle|e_0\rangle$ and $|1\rangle|e\rangle$ to $|1\rangle|e_1\rangle$ multiplies the system coherence by $\langle e_1|e_0\rangle$. 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.
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