Mueasurement-induced randomness in measured qubit processes

We discuss the effects of quantum measurement in a time series of qubits. We show that measurement generally induces high complexity in the observed classical time series and can both increase or decrease the inherent randomness (Shannon entropy rate) of the observed classical process with respect to the underlying stochastic process of qubits. We identify nonorthogonality of the qubit states as the mechanism underlying the resulting complexities and examine the influence of measurement choices on the randomness and structure of the measured qubit process. We discuss measurement choices of potential interest in gaining insight about the underlying time series of qubits.