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

Samuel P. Loomis, James P. Crutchfield
2019 Journal of statistical physics  
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more » ... fficial publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com". Abstract Among the predictive hidden Markov models that describe a given stochastic process, the -machine is strongly minimal in that it minimizes every Rényi-based memory measure. Quantum models can be smaller still. In contrast with the -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's circumstance.
doi:10.1007/s10955-019-02344-x fatcat:bh5mvmkzbjd4pgnbel7dvwqhxq