Open systems are described by density matrices evolving under completely positive trace-preserving maps. The Lindblad master equation is the standard Markovian generator: $$\frac{d\rho}{dt}=-\frac{i}{\hbar}[\hat H,\rho]+\sum_k\gamma_k\left(\hat L_k\rho\hat L_k^\dagger-\frac12\{\hat L_k^\dagger\hat L_k,\rho\}\right).$$

Measurement is not merely ignorance about preexisting values; it is an interaction that correlates system states with apparatus states. Interpretations differ on whether collapse is physical, effective, or purely epistemic.

Continuous monitoring can be modeled with stochastic unravelings of the master equation. This provides a bridge between conditioned dynamics, feedback control, and experimental readout.