Measuring qubits from finite-state controlled sources generically turns simple quantum processes into classical processes whose optimal predictors need an infinite number of states, a divergence traced to measurement-induced nonunifilarity.
(d) Mixed states for the stochastic process generated by (c) in that HMM’s state distribution simplex
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Measurement-Induced Randomness and Structure in Controlled Qubit Processes
Measuring qubits from finite-state controlled sources generically turns simple quantum processes into classical processes whose optimal predictors need an infinite number of states, a divergence traced to measurement-induced nonunifilarity.