This work introduces a new discrete framework that links the flow of information in weighted networks to emergent informational torsion and discrete closed timelike curves (CTCs). By connecting edge weights, dependent on mutual information, to Forman-Ricci curvature and defining persistent cycle circulations, we uncover self-sustained loops that act as discrete analogues of local causal reversals. Starting from multipartite quantum states represented as graphs, we show how specific entanglement patterns can generate effective geometric deformations. Promoting the model to a quantum formalism allows us to define curvature and circulation operators, giving a concrete way to study the quantum dynamics of these emergent structures. This framework provides a bridge between different areas of physics: quantum information theory, discrete geometry, and ideas of emergent gravity. It opens the door to exploring how entanglement and informational flows might shape causal structures, offering both conceptual insights and numerical tools that could inspire future developments in fundamental theory and quantum technologies.
This work introduces a new discrete framework that links the flow of information in weighted networks to emergent informational torsion and discrete closed timelike curves (CTCs). By connecting edge weights, dependent on mutual information, to Forman-Ricci curvature and defining persistent cycle circulations, we uncover self-sustained loops that act as discrete analogues of local causal reversals. Starting from multipartite quantum states represented as graphs, we show how specific entanglement patterns can generate effective geometric deformations. Promoting the model to a quantum formalism allows us to define curvature and circulation operators, giving a concrete way to study the quantum dynamics of these emergent structures. This framework provides a bridge between different areas of physics: quantum information theory, discrete geometry, and ideas of emergent gravity. It opens the door to exploring how entanglement and informational flows might shape causal structures, offering both conceptual insights and numerical tools that could inspire future developments in fundamental theory and quantum technologies.
This work presents a discrete informational model in which persistent flows of mutual information emerge within quantum entanglement networks, forming structures analogous to wormholes.The model links local informational curvature, defined through Forman-Ricci geometry, to the dynamics of information exchange between entangled nodes.Through discrete simulations on small graphs (triangular, quadrilateral, and dodecagonal), the study shows how stable circulation patterns of information can behave as “informational bridges,” connecting distant regions of the network.These results suggest a possible informational mechanism underlying the emergence of spacetime-like connectivity from quantum entanglement.
This paper presents a geometric–informational model of quantum decoherence formulated in terms of the Forman–Ricci curvature on a weighted graph representing correlations between entangled subsystems. In this framework, decoherence emerges as a curvature–driven process that progressively flattens the informational geometry of the system. The model derives a gradient–flow dynamics from an action principle with dissipation and is quantitatively compared with the experimental results of Bordes et al. (2024) on entangled gamma photons. The proposed formulation establishes a conceptual bridge between the Lindblad formalism and informational geometry, offering a scale–independent interpretation of quantum decoherence as the geometric relaxation of correlation structures, consistently describing both optical and gamma entanglement regimes.
Starting from the discrete spacetime structure predicted by loop quantum gravity (LQG), this paper constructs a universal model of quantum-dot information storage and systematically explores its logical correlation with time travel. We first formulate the discreteness of spacetime at the Planck scale and argue that the discrete spectra of geometric operators (area and volume) provide a natural quantized substrate for information storage. Crucially, we do not assert a direct physical isomorphism between Planck-scale spacetime quanta and mesoscopic quantum-dot spin states—a gap of roughly 26 orders of magnitude. Instead, using renormalization-group (RG) ideas and scale invariance, we reframe the link as a topological isomorphism of information structure and, operationally, as a quantum simulation: a quantum-dot array is a laboratory simulator of the discrete-spacetime information network rather than a physical counterpart of Planck-scale atoms. To address the causal paradoxes of closed timelike curves (CTCs), we propose a quantum-information self-consistency principle and connect it to Deutsch’s D-CTC model (1991; density-matrix fixed point) and the Lloyd et al. P-CTC model (2011; post-selected CTCs). We argue that spacetime discreteness supplies a natural ultraviolet cutoff which, together with non-local (entanglement-based) storage in the dot network, dissolves the grandfather paradox at the level of information. The metaphysical “isomorphism claim” is sharpened into a falsifiable “same-universality-class” hypothesis, accompanied by concrete criteria (entanglement-entropy scaling, power-law exponents, topological entanglement entropy). The proposed quantum-dot loop experiment is clarified as a quantum simulation of the information-propagation logic of CTCs, in the same paradigm as the Sycamore traversable-wormhole experiment (Jafferis et al., 2022), and is not a realization of macroscopic time travel. Building on the above, this paper advances two core theoretical constructs, each developed in a dedicated chapter. The first is the quantum-dot information-extension model (Chapter 8): the existence of a piece of spacetime information is identified with the existence of a timelike information world-tube—when information is created at an event, the quantum point carrying it extends along a timelike direction into a world-tube that persists until the information is erased. From this picture we derive a conservation law for the active quantum-point number density, a holographic–persistence capacity bound for the world-tube cross-section, and the thermodynamic costs of information creation, persistence, and annihilation. The second is the information dynamics of time travel (Chapter 9): within the world-tube language, two self-consistent routes for returning to the past are proposed—jumping to a parallel branch universe that already possesses a time machine (memory fully retained), or rewinding along one's own world-tube so that the extended quantum point recedes and annihilates at its initial event (entailing invalidation of downstream information, merging of the future and past operators' information, and the impossibility of retaining future memory). The two routes correspond respectively to cross-branch and same-branch fixed points of the causal-consistency functional. We emphasize that the pictures of Chapters 8 and 9 are theoretical hypotheses and conjectures proposed herein, intended to provide a mathematically self-consistent and in-principle falsifiable analytical framework rather than a claim about the physical realizability of time machines.
We propose a renormalization-group (RG) universality-class hypothesis linking the discrete-spacetime information network predicted by loop quantum gravity (LQG) to the entanglement network of a semiconductor quantum-dot array, deliberately avoiding any claim of microscopic isomorphism across the orders of magnitude separating the Planck and mesoscopic scales. Within this framework, Deutsch’s D-CTC and the Lloyd–Maccone post-selected (P-CTC) formulations of closed timelike curves (CTCs) are grounded on a discrete ultraviolet cutoff and non-local entanglement-based storage, and the area-law information capacity of the discrete network and the area-law entanglement of a gapped quantum-dot ground state are placed in the same universality class. We design a four-dot entanglement-loop quantum-simulation scheme—methodologically analogous to the Sycamore traversable-wormhole experiment of Jafferis et al.—for testing the information logic of CTCs on solid-state hardware, formulate explicit component-wise falsifiability criteria via a universality-class observable vector, and clearly delineate the epistemic boundary between substrate-independent universal-information claims (testable on the simulator) and substrate-specific quantum-gravity phenomenology (testable only by astrophysical means).
This paper proposes a novel theoretical framework based on discrete geometricflow and quantum state evolution to study topological phase transitions and theemergence of low-energy effective physics in quantum geometry. We construct discrete geometric dynamics on a three-dimensional periodic point cloud, driving edgelength evolution via the discrete Ricci flow equation, and attach a four-dimensionallocal Hilbert space to each edge, representing the quantum state of the system usingmatrix product states (MPS). Numerical simulations show that during the evolution of the discrete Ricci flow, the system undergoes a topological phase transitionat a specific curvature threshold, manifested as a jump in Betti numbers detectedby persistent homology. After the phase transition, the geometric mean curvature and the low-energy spectral gap of the quantum system synchronously entera plateau region, exhibiting a stable inverse relationship: ¯ ∆ = Λ/∥ ¯R∥+δ, whereΛ is an O(1) constant and δ is a small correction. This result, for the first timeat the numerical level, realizes a complete causal chain from pure geometric evolution to the generation of quantum low-energy parameters, providing a computableexample for the idea that ”geometric flow is renormalization group flow”.
Abstract This study examines closed timelike curves (CTCs) in quantum mechanics, focusing on the Deutsch model, one of the most widely studied frameworks for describing quantum systems in the presence of time loops. In this model, a quantum state ∣ψ⟩|\psi\rangle∣ψ⟩ interacts unitarily with its past version, effectively forming a two-qubit system where the chronologically consistent qubit interacts with a qubit ρCTC\rho_{\text{CTC}}ρCTC trapped in a closed timelike curve. The state ρCTC\rho_{\text{CTC}}ρCTC is determined by the Deutsch consistency condition, ensuring self-consistent evolution along the CTC. This approach allows for rigorous modeling of quantum systems under non-classical temporal structures, providing insights into temporal correlations, causality violations, and the potential computational advantages offered by CTC-assisted quantum operations. While alternative CTC models based on postselection have been proposed, the Deutsch model remains a foundational reference for studying quantum evolution in non-linear temporal frameworks. Its analysis informs research in quantum information, retrocausality, and the theoretical limits of computation in exotic spacetime geometries.