For disordered repeated quantum measurements with a unique stationary random state, the frequencies of every finite measurement-outcome word converge to the annealed stationary probability, for almost every disorder and almost every trajectory.
Exact endomorphisms of Lebesgue spaces
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Ergodic Theorems for Quantum Trajectories under Disordered Generalized Measurements
For disordered repeated quantum measurements with a unique stationary random state, the frequencies of every finite measurement-outcome word converge to the annealed stationary probability, for almost every disorder and almost every trajectory.