Beyond Locality: Unraveling Entanglement in Complex Quantum Systems

by

Author: Denis Avetisyan

New research explores how breaking the rules of local interactions impacts the fundamental properties of quantum entanglement.

Entanglement entropy scales with subsystem length, exhibiting a volume-law regime that expands with increasing nonlocality; specifically, stronger nonlocality—as evidenced by parameters up to $1000$—significantly enhances this volume-law scaling, sustaining it across a broader range of subsystem lengths and fundamentally altering the entanglement structure.
Entanglement entropy scales with subsystem length, exhibiting a volume-law regime that expands with increasing nonlocality; specifically, stronger nonlocality—as evidenced by parameters up to $1000$—significantly enhances this volume-law scaling, sustaining it across a broader range of subsystem lengths and fundamentally altering the entanglement structure.

This review investigates the entanglement structure of nonlocal field theories and the challenges they pose for holographic duality.

While established models of spacetime struggle to fully account for complex quantum correlations, this work, ‘Entanglement Structure of Nonlocal Field Theories’, investigates the impact of nonlocal interactions on entanglement within quantum field theories. Through numerical and holographic techniques, we demonstrate that nonlocality generates extensive entanglement alongside surprising features—including long-range correlations and a breakdown in the expected monogamy of entanglement—revealing a tension between field theory calculations and holographic descriptions. These findings suggest that conventional geometric frameworks may be insufficient to capture the intricate quantum states arising from nonlocal interactions, prompting the question of whether a fundamentally new approach is needed to fully understand the nature of these correlations.

Entanglement’s Nonlocal Signature

Quantum entanglement, a cornerstone of quantum mechanics, challenges classical locality. Characterizing its scaling—whether adhering to an ‘area law’ or a ‘volume law’—is crucial for understanding complex quantum systems. Recent research demonstrates a transition to volume-law entanglement for specific parameter regimes, contrasting with area laws. This suggests a fundamental shift in information encoding, demanding precise definitions to account for approximation noise.

Holographic computation of minimal surface area reveals a linear scaling with subsystem size for $d=2$ and $\omega=1$ at small nonlocality parameters (A=25, 30, 35), confirming a volume law, and this scaling persists with an enhanced slope for broader parameters (A=40, 60, 400), demonstrating the amplifying role of increasing A.
Holographic computation of minimal surface area reveals a linear scaling with subsystem size for $d=2$ and $\omega=1$ at small nonlocality parameters (A=25, 30, 35), confirming a volume law, and this scaling persists with an enhanced slope for broader parameters (A=40, 60, 400), demonstrating the amplifying role of increasing A.

Traditional methods struggle to characterize entanglement in many-body systems, necessitating innovative theoretical and computational approaches. These methods probe entanglement structure and reveal underlying physics, demanding rigorous definitions.

Nonlocality and the Emergence of Volume Law

Nonlocal field theories offer a framework where interactions aren’t limited by spatial proximity, predicting volume-law entanglement—scaling with system volume rather than boundary area. These theories are relevant for describing exotic states of matter, including Bose-Einstein condensates, exhibiting long-range entanglement and novel properties.

Mutual information between two disjoint intervals of equal length (l1=l2=10) exhibits a gradual decay with separation for moderate nonlocality parameters (A=40, 60, 80), highlighting persistent long-range correlations, while strong nonlocality (A=400, 600, 800) drastically slows this decay, maintaining substantial mutual information across a wide range of separations.
Mutual information between two disjoint intervals of equal length (l1=l2=10) exhibits a gradual decay with separation for moderate nonlocality parameters (A=40, 60, 80), highlighting persistent long-range correlations, while strong nonlocality (A=400, 600, 800) drastically slows this decay, maintaining substantial mutual information across a wide range of separations.

Characterizing entanglement in nonlocal field theories is computationally challenging. Advanced techniques—tensor networks, Monte Carlo simulations—are refined to address these complexities and push computational boundaries.

Simulating Quantum Correlations Numerically

Numerical lattice simulations quantify entanglement measures within nonlocal field theories, defining system dynamics through the Hamiltonian and utilizing covariance matrix techniques to efficiently compute entanglement entropy. This allows investigation of systems where analytical methods are limited.

Holographic mutual information and tripartite information, calculated for $d=2$ and $\omega=1$ with equal subsystem lengths of l=50, both undergo dramatic suppression as the nonlocality parameter A increases, with strong nonlocality (A=400) nearly eliminating both measures for all separations.
Holographic mutual information and tripartite information, calculated for $d=2$ and $\omega=1$ with equal subsystem lengths of l=50, both undergo dramatic suppression as the nonlocality parameter A increases, with strong nonlocality (A=400) nearly eliminating both measures for all separations.

Comparison of simulation results with theoretical predictions—particularly volume-law scaling—provides validation. Observed deviations or confirmations refine existing models and explore scenarios inaccessible to analytical calculations.

Holographic Duality and Correlational Discrepancies

The AdS/CFT correspondence establishes a duality between quantum field theories and gravity in Anti-de Sitter space, allowing study of strongly coupled field theories using classical gravity. Calculations utilize the Ryu-Takayanagi formula, relating entanglement entropy to minimal surface area.

Tripartite information $I_3$ for three disjoint regions is consistently negative for small, equal-length regions, confirming the monogamous nature of entanglement, and these negative values become significantly more pronounced with increasing separation and higher values of A for larger, equal-length regions.
Tripartite information $I_3$ for three disjoint regions is consistently negative for small, equal-length regions, confirming the monogamous nature of entanglement, and these negative values become significantly more pronounced with increasing separation and higher values of A for larger, equal-length regions.

Holographic calculations demonstrate a suppression of mutual and tripartite information as nonlocality increases, suggesting complete loss of long-range correlations. Conversely, field theory simulations maintain non-zero values, revealing a discrepancy in how correlations are represented within the holographic framework.

Towards a Complete Theory of Entanglement and Spacetime

Current investigations suggest a connection between quantum entanglement and spacetime geometry. Quantifying mutual information between multiple regions may reveal aspects of entanglement mirroring spacetime connectivity.

Tripartite information $I_3$ for three disjoint regions is consistently negative for small, equal-length regions, confirming the monogamous nature of entanglement, and these negative values become significantly more pronounced with increasing separation and higher values of A for larger, equal-length regions.
Tripartite information $I_3$ for three disjoint regions is consistently negative for small, equal-length regions, confirming the monogamous nature of entanglement, and these negative values become significantly more pronounced with increasing separation and higher values of A for larger, equal-length regions.

Further development of computational methods and holographic techniques is crucial. Advanced tensor network algorithms and numerical relativity simulations model complex entanglement structures. This research may unlock insights into quantum gravity and the emergence of spacetime, offering a pathway toward a consistent theory unifying quantum mechanics and general relativity.

The exploration of entanglement structure within nonlocal field theories demands a rigorous approach to verification, echoing a sentiment shared by the late Richard Feynman. He once stated, “The first principle is that you must not fool yourself – and you are the easiest person to fool.” This principle directly applies to the challenges presented by nonlocal systems; the extensive entanglement observed creates a tension with holographic duality because the duality struggles to accurately represent the full complexity of correlations. A seemingly ‘working’ holographic model, if not built upon strict mathematical grounding, risks self-deception, failing to capture the true nature of the entanglement structure and the underlying physics. The article’s focus on mutual and tripartite information serves as a crucial step in avoiding such folly, providing a more complete and provable picture of these complex systems.

The Horizon of Correlation

The observed tension between nonlocal field theories and holographic duality presents a challenge not merely to refinement of existing models, but to the very foundations of how information is encoded in quantum gravity. The insistence on volume-law scaling, while mathematically elegant, appears increasingly strained when confronted with the nuanced correlation structures arising from explicit nonlocality. Future investigations must move beyond simply ‘matching’ scaling laws; a demonstrable, provable equivalence – a true isomorphism – between the field theory and its holographic counterpart is the only acceptable resolution.

A fruitful avenue lies in a deeper exploration of multipartite entanglement. Tripartite information, and higher-order correlations, are not merely calculational hurdles, but potentially reveal fundamental constraints on the holographic mapping. The current formalism seems adept at capturing pairwise entanglement, but falters when confronted with genuinely complex, many-body correlations. A rigorous framework capable of characterizing such entanglement, and relating it directly to the geometry of the dual spacetime, remains conspicuously absent.

One suspects the difficulty isn’t a failure of mathematics, but a conceptual one. The pursuit of ‘holography’ may be misdirected if it presumes a simple, static correspondence. Perhaps information isn’t encoded on a boundary in the traditional sense, but dynamically emerges from its interaction with the bulk – a process requiring a formalism that transcends the limitations of current geometric approaches. The elegance of a provable solution, after all, is not in its simplicity, but in its necessity.

Original article: https://arxiv.org/pdf/2511.10505.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

See also:

2025-11-14 12:59