Strong and Weak Optimizations in Classical and Quantum Models of Stochastic Processes

08/26/2018

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by   Samuel Loomis, et al.

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Among the predictive hidden Markov models that describe a given stochastic process, the ϵ-machine is strongly minimal in that it minimizes every Rényi-based memory measure. Quantum models can be smaller still. In contrast with the ϵ-machine's unique role in the classical setting, however, among the class of processes described by pure-state hidden quantum Markov models, there are those for which there does not exist any strongly minimal model. Quantum memory optimization then depends on which memory measure best matches a given problem circumstance.