A Hidden Quantum Markov model framework for Entanglement and Topological Order in the AKLT Chain

Abstract: This paper introduces a hidden quantum Markov models (HQMMs) framework to the Affleck-Kennedy-Lieb-Tasaki (AKLT) state-a cornerstone example of a symmetry-protected topological (SPT) phase. The model's observation system is the physical spin-1 chain, which emerges from a hidden spin-1/2 layer through well-defined quantum emission operation. We show that the underlying Markov dynamics caputure maximal entanglement through the use of significant channels relevant to the AKLT state. We also show that SPT order induces a covariance on the observation decoding channels. This establishes an additional bridge between the quantum Machine learning and many-body physics, with promising implication in topological order and quantum information.