AKLT State is Indeed the Observation Process of a causal Hidden quantum Markov Model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911717691228160 |
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| author | Souissi, Abdessatar Andolsi, Amenallah |
| author_facet | Souissi, Abdessatar Andolsi, Amenallah |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_24431 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | AKLT State is Indeed the Observation Process of a causal Hidden quantum Markov Model Souissi, Abdessatar Andolsi, Amenallah Mathematical Physics 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. |
| title | AKLT State is Indeed the Observation Process of a causal Hidden quantum Markov Model |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2605.24431 |