Matrix Product States as Observations of Entangled Hidden Markov Models

• URL: http://arxiv.org/abs/2502.12641v1
• Date: Tue, 18 Feb 2025 08:44:17 GMT
• Title: Matrix Product States as Observations of Entangled Hidden Markov Models
• Authors: Abdessatar Souissi,
• Abstract summary: This paper reveals the intrinsic structure of Matrix Product States (MPS) by establishing their deep connection to entangled hidden Markov models (EHMMs)<n>It is demonstrated that a significant class of MPS can be derived as the outcomes of EHMMs, showcasing their underlying quantum correlations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper reveals the intrinsic structure of Matrix Product States (MPS) by establishing their deep connection to entangled hidden Markov models (EHMMs). It is demonstrated that a significant class of MPS can be derived as the outcomes of EHMMs, showcasing their underlying quantum correlations. Additionally, a lower bound is derived for the relative entropy between the EHMM-observation process and the corresponding MPS, providing a quantitative measure of their informational divergence. Conversely, it is shown that every MPS is naturally associated with an EHMM, further highlighting the interplay between these frameworks. These results are supported by illustrative examples from quantum information, emphasizing their importance in understanding entanglement, quantum correlations, and tensor network representations.

Related papers

• Hallucination Detection in LLMs via Topological Divergence on Attention Graphs [64.74977204942199]
  Hallucination, i.e., generating factually incorrect content, remains a critical challenge for large language models. We introduce TOHA, a TOpology-based HAllucination detector in the RAG setting.
  arXiv  Detail & Related papers  (2025-04-14T10:06:27Z)
• Sensitivity Meets Sparsity: The Impact of Extremely Sparse Parameter Patterns on Theory-of-Mind of Large Language Models [55.46269953415811]
  We identify ToM-sensitive parameters and show that perturbing as little as 0.001% of these parameters significantly degrades ToM performance. Our results have implications for enhancing model alignment, mitigating biases, and improving AI systems designed for human interaction.
  arXiv  Detail & Related papers  (2025-04-05T17:45:42Z)
• Dynamics of Matrix Product States in the Heisenberg Picture: Projectivity, Ergodicity, and Mixing [0.0]
  Matrix Product States (MPS) efficiently represent ground states of quantum many-body systems. 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. As an application, we analyze the depolarizing MPS, highlighting its lack of finite correlations and the need for an alternative ergodic description.
  arXiv  Detail & Related papers  (2025-03-09T10:36:04Z)
• Correlation hypergraph: a new representation of a quantum marginal independence pattern [0.0]
  We introduce a new representation of the patterns of marginal independence based on certain correlation hypergraphs.<n>We show that these correlation hypergraphs generalize to arbitrary quantum systems.<n>In the context of holography, we apply these techniques to derive a necessary condition for the realizability of entropy vectors.
  arXiv  Detail & Related papers  (2024-12-23T22:29:14Z)
• Correlations, Spectra and Entanglement Transitions in Ensembles of Matrix Product States [0.0]
  We investigate ensembles of Matrix Product States (MPSs) generated by quantum circuit evolution followed by projection onto MPSs with a fixed bond dimension $chi$.<n>In all cases, we analyze the spectra of the MPS transfer matrices and relate them to the spreading of mutual information in the MPS state.<n>We show the existence of a measurement-induced entanglement transition (MIPT) in MPS ensembles, with the averaged dimension of the transfer matrix's null space serving as the effective order parameter.
  arXiv  Detail & Related papers  (2024-12-18T19:00:33Z)
• General Framework for Quantifying Dissipation Pathways in Open Quantum Systems. II. Numerical Validation and the Role of Non-Markovianity [0.0]
  MQME-D allows us to decompose the overall energy dissipation process in open quantum system dynamics. We show that MQME-D accurately captures the contributions of specific bath components to the overall dissipation. Our work demonstrates that MQME-D combined with TSS can be reliably used to understanding how energy is dissipated in realistic open quantum system dynamics.
  arXiv  Detail & Related papers  (2024-06-01T02:11:36Z)
• Applications of flow models to the generation of correlated lattice QCD ensembles [69.18453821764075]
  Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables.
  arXiv  Detail & Related papers  (2024-01-19T18:33:52Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [43.80709028066351]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.<n>This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Quantum information spreading in random spin chains with topological order [0.0]
  Tripartite mutual information (TMI) based on operator-based entanglement entropy (EE) is an efficient tool for measuring them. We study random spin chains that exhibit phase transitions accompanying non-trivial change in topological properties. Quench dynamics of the EE and TMI display interesting behaviors providing essential perspective concerning encoding of quantum information.
  arXiv  Detail & Related papers  (2022-05-06T04:26:52Z)
• Three-fold way of entanglement dynamics in monitored quantum circuits [68.8204255655161]
  We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles. We obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements.
  arXiv  Detail & Related papers  (2022-01-28T17:21:15Z)
• Learning Multimodal VAEs through Mutual Supervision [72.77685889312889]
  MEME combines information between modalities implicitly through mutual supervision. We demonstrate that MEME outperforms baselines on standard metrics across both partial and complete observation schemes.
  arXiv  Detail & Related papers  (2021-06-23T17:54:35Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.