Structure of backward quantum Markov chains

This paper extended the framework of quantum Markovianity by introducing backward and inverse backward quantum Markov chains (QMCs). We established the existence of these models under general conditions, demonstrating their applicability to a wide range of quantum systems. Our findings revealed distinct structural properties within these models, providing new insights into their dynamics and relationships to finitely correlated states. These advancements contributed to a deeper understanding of quantum processes and have potential implications for various quantum applications, including hidden quantum Markov processes.