Degree of entanglement in Entangled Hidden Markov Models

Abstract

This paper investigates Entangled Hidden Markov Models (EHMMs), with a particular focus on how entanglement influences quantum dynamics. We present a structure theorem for inhomogeneous EHMMs, which provides a foundational understanding of their behavior in complex systems. Furthermore, we compute the Ohya degree of entanglement for models with deterministic stochastic matrices, offering a precise and rigorous way to quantify entanglement in these systems. By applying diagonal restrictions to the observation and hidden algebras, we also demonstrate how classical hidden Markov models (HMMs) naturally arise as a special case of EHMMs. This connection sheds light on the interplay between classical and quantum Markovian processes, bridging the gap between these two frameworks and deepening our understanding of their shared and distinct properties.