Simple and efficient solution of the identifiability problem for hidden Markov sources and quantum random walks

A solution of the identifiability problem (IP) for hidden Markov models (HMMs), based on a novel algebraic theory for random sources, is presented. It gives rise to an efficient and practical algorithm that can be easily implemented. Extant approaches are exponential in the number of hidden states and therefore only applicable to a limited degree. The algorithm can be equally applied to solve the IP for quantum random walks (QRWs) that have recently been presented as an analogon of Markov chains in quantum information theory. Moreover, the algorithm can be used to efficiently test HMMs and QRWs for ergodicity, which had remained an open problem so far.