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Internal Vacuum Gauge Structure as the Physical Origin of Quantum Entanglement

Bin Li

Published Feb 9, 2026• 0 citations
Publisher

Abstract

Quantum entanglement is conventionally characterized as a structural property of tensor-product Hilbert spaces, with limited emphasis on its geometric or gauge-theoretic organization. Within standard quantum field theory on a fixed classical spacetime background, we show that entanglement can be represented as a global compatibility constraint acting on internal degrees of freedom in the gauge-bundle formulation of the Standard Model. This representation is encoded by a vacuum-level internal gauge structure $\Xi(x)$ that is locally pure gauge, dynamically inert, and acts exclusively on internal fibers, leaving all local dynamics and the Standard Model Lagrangian unchanged. We formalize this perspective as a vacuum internal gauge structure (VIGS) and prove a corresponding structural result—the Vacuum Internal Gauge Theorem—which establishes that global compatibility relations associated with $\Xi$ act only on internal Hilbert-space factors and preserve locality and no-signaling within the regime considered here. The framework complements standard Hilbert-space and algebraic descriptions of entanglement by making explicit how global internal correlations can be organized geometrically without invoking nonlocal dynamics. Finally, we identify an experimentally accessible operational signature, based on correlated versus independent internal-frame scrambling, that distinguishes this geometric representation within existing entanglement platforms.

DOI
10.20944/preprints202512.0846.v2

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Quantum entanglement is conventionally characterized as a structural property of tensor-product Hilbert spaces, with limited emphasis on its geometric or gauge-theoretic organization. Within standard quantum field theory on a fixed classical spacetime background, we show that entanglement can be represented as a global compatibility constraint acting on internal degrees of freedom in the gauge-bundle formulation of the Standard Model. This representation is encoded by a vacuum-level internal gauge structure Ξ(x)\Xi(x)Ξ(x) that is locally pure gauge, dynamically inert, and acts exclusively on internal fibers, leaving all local dynamics and the Standard Model Lagrangian unchanged. We formalize this perspective as a vacuum internal gauge structure (VIGS) and prove a corresponding structural result—the Vacuum Internal Gauge Theorem—which establishes that global compatibility relations associated with Ξ\XiΞ act only on internal Hilbert-space factors and preserve locality and no-signaling within the regime considered here. The framework complements standard Hilbert-space and algebraic descriptions of entanglement by making explicit how global internal correlations can be organized geometrically without invoking nonlocal dynamics. Finally, we identify an experimentally accessible operational signature, based on correlated versus independent internal-frame scrambling, that distinguishes this geometric representation within existing entanglement platforms.
Entanglement is conventionally treated as an abstract property of tensor-product Hilbert spaces. We show instead that it can be realized as a global compatibility constraint in the internal gauge bundle of the vacuum, encoded by a locally pure-gauge field Ξ(x) acting only on internal degrees of freedom. This vacuum internal gauge symmetry (VIGS) yields a concrete, symmetry-based mechanism for quantum correlations that requires no nonlocal dynamics, introduces no new particles or forces, and leaves the Standard Model Lagrangian unchanged. Our main result is the Vacuum Internal Gauge Theorem, which demonstrates that: (i) all nontrivial global constraints induced by Ξ are confined to internal fibers; (ii) only internal degrees of freedom can become entangled; (iii) no information can be transmitted via the vacuum gauge structure; and (iv) gravitational degrees of freedom, having no internal fiber structure, cannot be entangled. Thus VIGS explains the empirical restriction of entanglement to internal DOFs and predicts the absence of gravitational entanglement, providing a gauge-theoretic foundation for quantum correlations within a strictly local spacetime.
Quantum information has become a powerful tool for probing the structure of quantum field theories, yet its application to gauge theories remains subtle. On the one hand, quantum information theory assumes subsystem locality, i.e.~the factorization of the total Hilbert space into subsystems. On the other hand, gauge constraints prevent the total Hilbert space to decompose into a spacetime-local tensor product structure. Because the Hilbert space structure of gauge theories does not accommodate the subsystem decomposition used in quantum information theory, standard information-theoretic results, such as the Local Operations and Classical Communication (LOCC) theorem, cannot be used straightforwardly in the context of gauge theories. In this work, we bridge this gap in the case of a two-dimensional lattice gauge model that captures key features of electromagnetism. In particular, we construct gauge-invariant local algebras and derive a physically meaningful decomposition of the Hilbert space, providing an operationally consistent notion of locality in the absence of a local tensor-product structure. We apply this framework to field-mediated entanglement protocols relevant to proposed tests of the quantum nature of gravity. We show that the discretized version of electromagnetism satisfies an analogue of the LOCC theorem: entanglement cannot be generated without genuine quantum field interactions, even in the absence of a spacetime-local tensor product factorization of the Hilbert space. This may point towards an operational way to define a subsystem structure for gauge theories.
Quantum information has become a powerful tool for probing the structure of quantum field theories, yet its application to gauge theories remains subtle. On the one hand, quantum information theory assumes subsystem locality, i.e.~the factorization of the total Hilbert space into subsystems. On the other hand, gauge constraints prevent the total Hilbert space to decompose into a spacetime-local tensor product structure. Because the Hilbert space structure of gauge theories does not accommodate the subsystem decomposition used in quantum information theory, standard information-theoretic results, such as the Local Operations and Classical Communication (LOCC) theorem, cannot be used straightforwardly in the context of gauge theories. In this work, we bridge this gap in the case of a two-dimensional lattice gauge model that captures key features of electromagnetism. In particular, we construct gauge-invariant local algebras and derive a physically meaningful decomposition of the Hilbert space, providing an operationally consistent notion of locality in the absence of a local tensor-product structure. We apply this framework to field-mediated entanglement protocols relevant to proposed tests of the quantum nature of gravity. We show that the discretized version of electromagnetism satisfies an analogue of the LOCC theorem: entanglement cannot be generated without genuine quantum field interactions, even in the absence of a spacetime-local tensor product factorization of the Hilbert space. This may point towards an operational way to define a subsystem structure for gauge theories.
This work presents an effective theoretical framework in which quantum dynamics emerges from a homogeneous scalar compression field endowed with an internal infinite structure. The model reproduces Schrödinger-type dynamics, the continuity equation, and the quantum potential as structural consequences of the underlying field description. Within this formulation, the Born rule arises as an equilibrium condition associated with coarse-graining over unresolved internal degrees of freedom rather than as a fundamental postulate. The same field structure naturally admits a vacuum energy interpretation consistent with dark energy phenomenology. Additionally, under a conformal effective metric hypothesis, the framework yields an emergent gravitational sector compatible with the weak-field parametrized post-Newtonian (PPN) limit, reproducing standard results for light deflection, Shapiro time delay, and perihelion precession at leading order. The theory preserves local dynamical evolution while allowing globally correlated states, providing an alternative interpretational perspective consistent with effective field theory principles. The work is positioned as a foundational and conceptual investigation rather than a replacement for established quantum or gravitational theories.
Quantum entanglement is commonly characterized through global state descriptions on tensor product spaces, correlation measures or algebraic constructions, while local consistency constraints play no explicit structural role. We formulate entanglement as a combinatorial structure of overlapping local descriptions, drawing on De Bruijn graphs, where nodes represent overlapping contexts and paths encode globally coherent assemblies. We construct a graph whose nodes represent reduced quantum states on subsystems of fixed size and whose edges encode admissible extensions consistent with quantum mechanical compatibility conditions. Global many body states correspond to paths on this graph, while entanglement is reinterpreted as a property of graph connectivity and path multiplicity, rather than as a standalone numerical quantity. This formalism allows a separation between constraints imposed purely by local quantum consistency and additional structure introduced by dynamics, symmetries or boundary conditions, also clarifying how large-scale structural features may arise from local compatibility alone. Our graph-based formulation provides several advantages over conventional approaches. Supporting a unified treatment of static entanglement structure and dynamical evolution, it incorporates finite order locality and memory effects. Entanglement growth can be interpreted as path proliferation, while decoherence and noise correspond to the removal of admissible transitions. Our approach leads to testable hypotheses concerning the scaling of admissible state extensions, the robustness of entangled structures under local perturbations and the emergence of effective geometry from overlap constraints. Potential future directions include applications to many body reconstruction problems and comparative analysis of different classes of quantum states within a single combinatorial language.
In gauge theories the presence of constraints can obstruct expressing the global Hilbert space as a tensor product of the Hilbert spaces corresponding to degrees of freedom localized in complementary regions. In algebraic terms, this is due to the presence of a center---a set of operators which commute with all others---in the gauge invariant operator algebra corresponding to a finite region. A unique entropy can be assigned to algebras with a center, giving a place to a local entropy in lattice gauge theories. However, ambiguities arise on the correspondence between algebras and regions. In particular, it is always possible to choose (in many different ways) local algebras with a trivial center, and hence a genuine entanglement entropy, for any region. These choices are in correspondence with maximal trees of links on the boundary, which can be interpreted as partial gauge fixings. This interpretation entails a gauge fixing dependence of the entanglement entropy. In the continuum limit, however, ambiguities in the entropy are given by terms local on the boundary of the region, in such a way relative entropy and mutual information are finite, universal, and gauge independent quantities.