Lorentzian Threads in Holography Enable Nonlocal Computation, yet Fail to Account for Negativity in Mutual Complexity
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The fundamental connection between gravity and quantum information continues to yield surprising insights, and recent work explores how computations within quantum field theories can appear local from the perspective of a higher-dimensional gravitational system. Elena Cáceres from The University of Texas at Austin, Rafael Carrasco and Juan F. Pedraza from Instituto de Física Teórica UAM/CSIC, investigate the ability of established holographic complexity proposals to support this idea, focusing on the Complexity=Volume approach. Their analysis reveals limitations in current methods when examining the complexity of quantum subsystems, specifically an inability to account for certain measures of quantum entanglement. To overcome this, the team proposes a modified framework using multiple types of ‘Lorentzian threads’, demonstrating that a successful implementation requires additional computational gates capable of performing nonlocal operations within the corresponding quantum field theory, suggesting a deeper connection between spacetime geometry and the fundamental limits of computation. Gravity, Quantum Information, and Holography This extensive collection of citations details research in theoretical physics, particularly exploring connections between quantum gravity, quantum information theory, and the fundamental nature of spacetime. Many studies focus on holographic principles, entanglement entropy, and the Ryu-Takayanagi formula, investigating how information is encoded in gravitational systems. Research also delves into black hole entropy, information loss, and the structure of black holes, seeking to understand these enigmatic objects. Investigations into Conformal Field Theory (CFT) and its role in the AdS/CFT correspondence are prominent, alongside rigorous mathematical analyses utilizing convex optimization and measure theory. Key themes emerge from this body of work, including the intriguing connection between Einstein-Rosen bridges (wormholes) and quantum entanglement, known as ER=EPR. Researchers are also exploring how concepts from complexity theory can illuminate the holographic principle, and how quantum error correction might resolve paradoxes in black hole physics. Attempts to reconstruct spacetime geometry from quantum entanglement are central, alongside efforts to resolve the information paradox in black hole evaporation. This bibliography represents a highly active and cutting-edge area of research, bridging the gap between seemingly disparate fields.
Lorentzian Threads Capture Mutual Complexity Relationships The study investigates holographic complexity, examining whether current methods accurately reflect computations within a theoretical framework connecting gravity and quantum field theory. Researchers focused on the Complexity=Volume (CV) proposal and its application to calculating complexity in subsystems, discovering limitations in standard approaches when analyzing relationships between these subsystems. To address this, scientists modified the Lorentzian threads program, introducing multiple ‘flavors’ of threads to represent different computational pathways. This involved defining distinct regions within the theoretical space and constructing ‘domains of dependence’ that delineate areas influenced by specific calculations.
The team formulated a program to minimize the total number of threads required to perform computations across these regions, subject to constraints ensuring sufficient computational resources. Initial attempts revealed a contradiction with the CV proposal, which predicts a superadditive relationship between the complexity of subsystems. This prompted the development of a more generalized framework utilizing multiple thread flavors. Researchers introduced two distinct measures, μ1 and μ2, each associated with a specific thread flavor and dedicated to calculating complexities related to different subregions. These thread flavors were visualized as pathways within a theoretical manifold.
The team then formulated a program to simultaneously calculate the complexities of both subregions and their union, minimizing the total number of threads while adhering to constraints. This program, incorporating a factor of 1/2 to account for shared computational resources, aimed to resolve the contradiction and provide a more accurate representation of complexity relationships. The resulting Lagrangian incorporates these measures and constraints, enabling the calculation of complexities across systems with an arbitrary number of subregions.
Lorentzian Threads Fail Subsystem Complexity Analysis Recent work in holography suggests that certain complex systems can perform computations in a way that appears local from a broader perspective, even if the underlying processes are nonlocal.
This research investigates how well current methods for calculating holographic complexity support this idea, specifically focusing on the Complexity=Volume proposal. Scientists reformulated this proposal using Lorentzian threads, which represent computations as being performed with local operations. However, standard Lorentzian threads proved inadequate when analyzing the complexity of subsystems and their relationships.
The team discovered that the original methods could not account for ‘mutual complexity’. To address this, researchers modified the Lorentzian threads program by introducing multiple ‘flavors’ of threads, effectively expanding the computational possibilities within the model. Analysis revealed that an optimal solution using these multiple thread types implies the existence of additional types of computational gates, enabling nonlocal computations within the dual system. This suggests that the system’s computational power is greater than previously understood.
The team proposes interpreting this multi-flavor program in terms of Lorentzian ‘hyperthreads,’ drawing an analogy to similar concepts in Riemannian geometry. This work establishes a framework for understanding how complexity arises in holographic systems, potentially offering insights into the nature of computation itself.
The team’s calculations demonstrate that the objective function, minimized under specific constraints, yields a solution where the density of threads satisfies a crucial condition, ensuring a non-vanishing flux through the boundary and maintaining the system’s homology. Further analysis confirms that the solution is equivalent to satisfying specific conditions related to a function, demonstrating a rigorous mathematical foundation for the proposed model.
Multiple Thread Flavors Resolve Complexity Negativity Recent research has focused on understanding how holographic complexity, a measure of the computational resources needed to describe a system, relates to the geometry of spacetime. Scientists investigated the Complexity=Volume proposal, discovering limitations in its standard formulation when applied to subsystems, specifically its inability to account for ‘negativity’ in ‘mutual complexity’. To address this issue, researchers modified the existing framework by introducing the concept of ‘multiple thread flavors’, assigning different types of Lorentzian threads to different subregions of the system.
The team demonstrated that an optimal solution using these multiple thread flavors necessitates the existence of additional computational gates within the dual quantum field theory, implying that computations can occur in a non-local manner. This suggests a richer computational structure than previously understood, linking the geometry of spacetime to the fundamental operations within the quantum system. The authors acknowledge that their current formulation is a step towards a more complete theory and that further work is needed to fully explore its implications, focusing on developing a more general formulation that reveals deeper connections between gravity, quantum information, and the nature of computation. 👉 More information 🗞 Lorentzian threads and nonlocal computation in holography 🧠 ArXiv: https://arxiv.org/abs/2512.07963 Tags: