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.
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.
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.
Local quantum interactions generate dynamics in an exponentially large Hilbert space, yet locality and entanglement restrict the information that can spread and accumulate. Bounds on propagation and entanglement growth, together with tensor networks, exploit these restrictions to discard information unnecessary for describing the evolution. This leads to a sharper question: how much information must any low-rank representation retain? Here we determine these limits, up to logarithmic factors, for short-range interactions. For time-independent evolution, the optimal rank obeys logD=O(t+log(1/ε)), with matching lower bounds fixing the accuracy exponent 1/2; for arbitrary driving, matching fixed-time bounds instead give 2/3. Correspondingly, the corresponding dynamical entanglement spectra exhibit distinct small-α Rényi laws, α−1 and α−2. In one dimension, the static limit is constructively attained by an explicit MPO algorithm, with an analogous extension to Liouvillian dynamics. Together, these results determine the irreducible information required to represent local quantum evolution and uncover distinct entanglement structures in static and driven dynamics.
We introduce a lattice-theoretic framework for composite information systems in which tensor-like composition and entanglement are defined without presupposing Hilbert spaces or quantum states. Starting from approximation operators induced by indiscernibility relations, we construct composite systems via interaction-dependent closure operators and characterize their fixed-point lattices. Entanglement is defined structurally as the impossibility of generating a fixed point of the composite system from local fixed points alone. This notion does not rely on non-distributive logic a priori and remains meaningful even when local lattices are Boolean. Non-distributive and orthomodular structures arise only under additional conditions and are treated as emergent properties rather than assumptions. The proposed framework generalizes the concept of entanglement as a property of composition and interaction, providing a unified information-theoretic perspective on non-separability beyond standard quantum-mechanical formalisms. By mapping quantum states to correlation patterns via row-set tensor products, we demonstrate that standard quantum entanglement can be understood as a stabilized structural constraint. In this context, maximally entangled states, such as Bell states, correspond to diagonal constraint sets that are non-generable from local components, confirming that the structural core of entanglement exists independently of linear or probabilistic interpretations. Beyond quantum mechanics, the framework admits a natural interpretation in terms of relational databases, where entanglement corresponds to irreducible global relations stabilized by interaction-induced fixed points.
Quantum entanglement violates Bell inequalities experimentally, ruling out locally closed descriptions of physical systems. This violation is not dynamical—no superluminal signaling occurs—but structural: the global quantum state cannot be reconstructed from local properties. We formalize this failure of local closure using the Theory of Axiomatic Necessity (TNA), where coherent systems require irreducible external structural support (N₁) beyond their locally observable domain (N₀). Entanglement provides a physical instantiation of this principle: the global wavefunction plays a role structurally analogous to N₁, enabling coherence without operating causally. This framework unifies quantum non-separability with similar structural limits in mathematics, machine learning, and social systems, demonstrating that local closure is not merely difficult but impossible for coherent systems.
We propose Stratified Causal Actualization (SCA), a generative framework in which physical reality is not presupposed as spacetime populated by matter, nor as probabilistic outcomes governed by dynamical laws, but as the irreversible actualization of causally constrained possibility. Beginning from primitive events and a causality relation devoid of geometry, time, or metric structure, we construct an ordinally stratified latent causal space encoding structured potentiality. We show that physics cannot be written directly on this space: realization requires an epistemic projection that discards internal causal structure while preserving distinguishability, yielding a realizability domain Ω. On Ω we derive admissibility, filtration, valuation, and variational actualization, closing the schema (Ω,A,⪯,ρ,TA,W,Φ,JA,D) governing consistent realization. A central result is the identification of a universal causal saturation invariant: the ratio of actual to maximal admissible causal restructuring. This invariant underlies the observed invariance of light propagation without presupposing spacetime geometry or kinematic postulates, and generates causal horizons as structural, rather than geometric, phenomena. Within this framework, time emerges as restriction depth, distance as constraint-mediated reachability, matter as stable restriction cores, and physical law as the fixed-point structure of permissible actualization. General relativity and quantum mechanics arise as complementary representational regimes encoding different projections of the same underlying causal stratification. SCA does not modify existing physical theories; it identifies the landscape from which their core structures necessarily arise.
ENG: This work explores whether the foundational difficulties of quantum theory originate not from incomplete dynamics, but from insufficiently constrained notions of local description. This work develops a structural framework for quantum theory based on constraints on admissible local descriptions rather than on modified dynamics or additional physical laws.Starting from a global quantum state defined on a C∗^*∗-algebra of observables, we introduce the space of factorizations as possible local descriptions and define a structural cost functional measuring their non-separability. A principle of structural stability is proposed: physically persistent descriptions correspond to (local) minima of the cost functional. Under general assumptions—nullity on separable states, invariance under local automorphisms, additivity for independent systems, and local regularity—the cost is shown to be uniquely characterized (up to a constant) by algebraic mutual information. The framework provides a unified structural account of quantum probability, effective collapse, irreversibility, and the emergence of classicality, without violating global unitarity. Geometric structures arise naturally from the second variation of the cost on the space of factorizations, while time and causality appear as effective notions associated with sequences of stable descriptions. The approach does not assume spacetime, locality, or causality as primitives, and clarifies the domains where local descriptions fail, including regimes with infinite entanglement or algebraic type III structures. The work positions structural constraints as a foundational layer underlying quantum mechanics and emergent geometry, while explicitly identifying its mathematical limits and open problems. ITA: Questo lavoro esplora se le difficoltà fondamentali della teoria quantistica non derivano da dinamiche incomplete, ma da nozioni di descrizione locale non sufficientemente vincolate. Questo lavoro sviluppa un quadro strutturale per la teoria quantistica basata su vincoli su descrizioni locali ammissibili piuttosto che su dinamiche modificate o leggi fisiche aggiuntive. Partendo da uno stato quantistico globale definito su un C ∗ ^* ∗ -algebra degli osservabili, introduciamo lo spazio delle fattorizzazioni come possibili descrizioni locali e definiamo un funzionale di costo strutturale che misura la loro non separabilità. Viene proposto un principio di stabilità strutturale: le descrizioni fisicamente persistenti corrispondono ai minimi (locali) del funzionale di costo. Sotto ipotesi generali – nullità su stati separabili, invarianza per automorfismi locali, additività per sistemi indipendenti e regolarità locale – si dimostra che il costo è caratterizzato in modo univoco (a meno di una costante) da informazione mutua algebrica. Il quadro fornisce una spiegazione strutturale unificata della probabilità quantistica, del collasso effettivo, dell'irreversibilità e dell'emergere della classicità, senza violare l'unitarietà globale. Le strutture geometriche emergono naturalmente dalla seconda variazione del costo sullo spazio delle fattorizzazioni, mentre tempo e causalità appaiono come nozioni effettive associarsi a sequenze di descrizioni stabili. L'approccio non presuppone che spaziotempo, località o causalità siano primitivi e chiarisce i domini in cui le descrizioni locali falliscono, inclusi i regimi con entanglement infinito o strutture algebriche di tipo III. Il lavoro posiziona i vincoli strutturali come uno strato fondamentale alla base della meccanica quantistica e della geometria emergente, identificandone esplicitamente i limiti matematici ei problemi aperti.