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Paper VI — Entanglement Information Locality and Many-Body Structure

Paul Cooney

Published Dec 14, 2025• 0 citations
Publisher

Abstract

Paper VI — Entanglement Information Locality and Many-Body Structure DescriptionThis work extends ordered-dynamics locality principles to composite systems, deriving entanglement structure and many-body correlations from operational constraints. Entanglement emerges as a necessary feature of jointly constrained information propagation, not as an added axiom. The paper clarifies the operational meaning of non-separability and establishes the foundations for multi-particle quantum structure within the ODRP. Keywordsentanglement; many-body systems; quantum correlations; operational locality; information theory; quantum foundations

DOI
10.5281/zenodo.17925691

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Paper VI — Entanglement Information Locality and Many-Body Structure DescriptionThis work extends ordered-dynamics locality principles to composite systems, deriving entanglement structure and many-body correlations from operational constraints. Entanglement emerges as a necessary feature of jointly constrained information propagation, not as an added axiom. The paper clarifies the operational meaning of non-separability and establishes the foundations for multi-particle quantum structure within the ODRP. Keywordsentanglement; many-body systems; quantum correlations; operational locality; information theory; quantum foundations
Paper IV — Local Interactions and Potentials from Operational Locality DescriptionThis paper shows how local interaction terms and effective potentials arise from operational locality constraints. By analyzing admissible deformations of free ordered dynamics, we derive interaction structure without invoking classical force laws or background geometry. The results clarify why local potentials dominate physical dynamics and how interaction terms reflect operationally constrained information exchange. Keywordslocal interactions; emergent potentials; operational physics; quantum dynamics; reconstruction theory; locality
Paper IV — Local Interactions and Potentials from Operational Locality DescriptionThis paper shows how local interaction terms and effective potentials arise from operational locality constraints. By analyzing admissible deformations of free ordered dynamics, we derive interaction structure without invoking classical force laws or background geometry. The results clarify why local potentials dominate physical dynamics and how interaction terms reflect operationally constrained information exchange. Keywordslocal interactions; emergent potentials; operational physics; quantum dynamics; reconstruction theory; locality
Recent works in foundations of quantum (field) theory and relativistic quantum information try to better grasp the interplay between the structure of quantum correlations and the constraints imposed by causality on physical operations. Chapter 1 is dedicated to the study of the conceptual implications of quantum nonlocality, a concept that subsumes that of entanglement in a certain way. We detail the recent information-theoretic approaches to understanding the structure of nonlocal correlations, and the issues the latter raise concerning the ability of local observers to isolate a system from its environment. Chapter 2 reviews in what sense imposing Poincare invariance affects entanglement detection and quantification procedures. This invariance ultimately forces a description of all quantum systems within the framework of quantum field theory, which leads to the impossibility of localized finite-energy states and to the divergence of all entanglement measures for local observers. We provide a solution to these two problems by showing that there exists a generic equivalence between a finite spatial resolution of the measurement apparatus and the exclusion of high-energy degrees of freedom from the definition of the observed system. This equivalence allows for an epistemic interpretation of the standard quantum formalism describing nonrelativistic localized systems and their correlations, hence a clarification of the origin of the finite measures of entanglement between such systems. Chapter 3 presents a recent theoretical framework that predicts the existence of correlations with indefinite causal order. In analogy to the information-theoretic approaches to nonlocal correlations, we introduce some principles that constrain the structure of such correlations, which is a first step toward a clear understanding of their physical origin.
We study entanglement reachability in quantum many-body systems evolving under physically admissible local dynamics. While Lieb--Robinson bounds constrain the propagation of information, and complexity-based approaches characterize the resources required to represent or prepare quantum states, these frameworks do not by themselves determine which entanglement structures are dynamically attainable. The central question addressed in this work is therefore: which entanglement structures can arise under constrained quantum evolution, and which remain inaccessible despite being kinematically allowed? We introduce a unified axiomatic framework for entanglement reachability based on the notion of \emph{structural confinement}. The framework incorporates finite-range locality, finite-dimensional memory degrees of freedom, and abstract representability constraints expressed through operator subsystems. Rather than characterizing accessibility directly in Hilbert space, we formulate the problem on an induced structural space of entanglement configurations and quantum information patterns. We establish a structural confinement theorem showing that admissible dynamics generate only a restricted reachable region in structural space. The theorem provides a general criterion for identifying forbidden structures whenever their defining information cannot be preserved within the admissible representational framework. Thus, ocality, memory, and representability constraints do not merely limit the rate of information propagation; they impose additional dynamical restrictions on the set of quantum structures that can actually be realized. The generality of the framework is demonstrated through three explicit realizations involving multipartite coherence, tensor-network representability, and protected logical nformation in quantum error-correcting codes. Although these realizations involve distinct physical structures, they are governed by the same underlying confinement mechanism: dynamical accessibility is determined by the compatibility between physical evolution and the structural information retained by the chosen representation. These results establish structural confinement as a general organizing principle for entanglement reachability under constrained quantum dynamics. The framework provides a unified language for deriving dynamical accessibility limits beyond propagation bounds alone and for classifying which quantum structures are reachable, forbidden, or conditionally accessible in locally constrained many-body systems.
The aim of this dissertation is to clarify the structure of entanglement, a type of quantum correlations, in various quantum systems with a large number of degrees of freedom for holography between generic quantum systems and spacetimes toward a quantum description of our universe. Previous examinations of entanglement and holography have focused on specific classes of quantum systems due to the lack of computational techniques in field theory and the inherent limitation of holography. This dissertation informs various methods and formalisms to overcome these difficulties by extending the target quantum systems with mass and interactions, boundaries, and geometric variational ansatze. These approaches provide insights into the generalization of holography from the bottom up. This dissertation initiates a comprehensive study beyond conventional holography by establishing new techniques in quantum field theory, holography, and tensor networks. Focusing on entanglement entropy, we found it is generally expressed in terms of renormalized two-point correlators of both fundamental and composite operators. Beyond entanglement entropy, we found the operational meaning of the entanglement structure in generic tensor networks. Furthermore, we established a correct prescription for the AdS/BCFT correspondence with a local operator quench.
This document is part of the Informational Mechanics (IM) framework and is published in the IM-D (Core Physics) series within the IM v0.3 corpus. The paper develops a structural account of quantum entanglement under regime-limited admissibility constraints. Rather than introducing new dynamics, hidden variables, or collapse mechanisms, it analyzes entanglement as a consequence of structural non-factorizability arising from bilinear composition and tensor minimality within admissible operator regimes. Building on IM-B004 (tensor minimality), IM-C004 (regime-conditional structural principles), and IM-E004 (operator-defined outcome weights), the analysis shows that Bell-inequality violations constrain classical factorizability assumptions without implying superluminal signaling or ontological inseparability. The account preserves the formal structure of quantum mechanics and treats locality and no-signaling conditions as operator-level constraints. No new axioms, empirical fits, or modifications to established physical theories are introduced. The contribution is classificatory and structural: it clarifies how entanglement and Bell correlations emerge within regime-bounded admissibility while explicitly identifying the structural assumptions under which the account would require revision.