arXiv subjects

Amenallah Andolsi

Publications and source records attributed to Amenallah Andolsi.

4 recordsLinked to original sources

arXiv2026

AKLT State is Indeed the Observation Process of a causal Hidden quantum Markov Model

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.

math-ph↗

arXiv2025

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

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.

quant-ph↗

arXiv2025

Dynamics of Matrix Product States in the Heisenberg Picture: Projectivity, Ergodicity, and Mixing

This paper introduces a Heisenberg picture approach to Matrix Product States (MPS), offering a rigorous yet intuitive framework to explore their structure and classification. MPS efficiently represent ground states of quantum many-body systems, with infinite MPS (iMPS) capturing long-range correlations and thermodynamic behavior. We classify MPS into projective and non-projective types, distinguishing those with finite correlation structures from those requiring ergodic quantum channels to define a meaningful limit. Using the Markov-Dobrushin inequality, we establish conditions for infinite-volume states and introduce ergodic and mixing MPS. As an application, we analyze the depolarizing MPS, highlighting its lack of finite correlations and the need for an alternative ergodic description. This work deepens the mathematical foundations of MPS and iMPS, providing new insights into entanglement, phase transitions, and quantum dynamics.

math-ph↗

arXiv2024

Matrix Product States in Quantum Spin Chains

In this work, we present a novel representation of matrix product states (MPS) within the framework of quasi-local algebras. By introducing an enhanced compatibility condition, we enable the extension of finite MPS to an infinite-volume state, providing new insights into complex, high-dimensional quantum systems. As an illustrative example, we apply this method to the Greenberger-Horne-Zeilinger (GHZ) state. This approach offers significant potential for advancing theoretical frameworks and practical methodologies in the field of quantum information.

quant-ph↗