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arXiv:2502.12641 · Journal of Statistical Physics

Matrix Product States as Observations of Entangled Hidden Markov Models

Abdessatar Souissi

Published Jun 16, 2025• 4 citations
arXivHTMLPDF
DOI
10.1007/s10955-025-03472-3

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We present a rigorous formulation of the spin-1 Affleck--Kennedy--Lieb--Tasaki (AKLT) state within the framework of hidden quantum Markov models (HQMMs). We show that the AKLT ground state admits a natural representation as the observable output of a causal HQMM, thereby endowing it with an underlying hidden quantum memory that is fully consistent with its standard finitely correlated (matrix product state) description. This viewpoint yields a compact and structurally transparent characterization of the AKLT chain as a quantum spin system equipped with intrinsic quantum memory. Our results further indicate that the HQMM framework provides a promising setting for analyzing measurement-based quantum computation (MBQC) and related information-processing tasks.