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.
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.
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 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.
The mathematical operation involved in quantum--classical limits constitutes an active research area. The limit is usually associated with semiclassical expansions or environment-induced decoherence. In this work we argue that a complementary and conceptually sharp characterization is available: the quantum--classical transition can be understood as a flattening of the information geometry underlying quantum state space. From this perspective, \textbf{quantumness is associated with curvature-induced rigidity of probability assignments}, while classical behavior emerges when this geometric rigidity becomes operationally irrelevant. This geometric viewpoint provides a structural criterion for classicality based on the scalar curvature of the information metric and unifies semiclassical limits, decoherence, and thermodynamic coarse-graining within a single framework.
Tri-Wave Geometry of Quantum Information: Curvature, Reciprocity, and Emergent Structure introduces a unified mathematical framework that links quantum information, quantum field theory, complexity dynamics, and gravitational geometry through three fundamental operators: curvature reciprocity , and log-log emergence. The paper develops these operators from first principles and demonstrates how their interaction gives rise to quantum behavior, information flow, multi-scale structure, and the geometry of spacetime. The Tri-Wave model reframes several core concepts in physics—including entanglement, renormalization, complexity growth, and curvature—as manifestations of a single underlying geometric structure. Applications to quantum computing, QFT, and gravity are explored, along with implications for quantum measurement, superposition, and the informational foundations of physical law. The manuscript was developed through a novel human–AI collaborative methodology, blending human conceptual exploration with AI-assisted mathematical refinement and structural articulation. This work stands as an early example of AI-augmented theoretical research and offers a potential foundation for future inquiry into information-based interpretations of quantum mechanics and geometric unification.
The process of quantum measurement is known to induce decoherence in the measured system. In this work we propose that the rate of decoherence, denoted by γ, can be expressed as a function of the geometric properties of the underlying quantum state manifold, γ = f(G). Here G represents a scalar or tensorial quantity that quantifies the curvature, volume, or other intrinsic geometrical features of the state space. We develop a general framework that connects the measurement operators, the dynamical evolution of the density matrix, and the geometry of the space of pure states. By treating the measurement process as a stochastic dynamical map acting on the Bloch sphere for two-level systems and on the complex projective space CP^(N−1) for N-level systems, we derive explicit forms of f(G) that depend on the sectional curvature and the Fubini–Study metric. The resulting theory predicts that states situated in highly curved regions of the state space will exhibit accelerated decoherence compared to states in flatter regions. This geometric damping mechanism offers a novel perspective on the measurement problem and suggests new strategies for protecting quantum coherence by engineering state-space geometry. The potential for a Nobel Prize arises from the fundamental shift in understanding that geometry, rather than only dynamics, can control quantum measurement outcomes.
The process of quantum measurement is known to induce decoherence in the measured system. In this work we propose that the rate of decoherence, denoted by γ, can be expressed as a function of the geometric properties of the underlying quantum state manifold, γ = f(G). Here G represents a scalar or tensorial quantity that quantifies the curvature, volume, or other intrinsic geometrical features of the state space. We develop a general framework that connects the measurement operators, the dynamical evolution of the density matrix, and the geometry of the space of pure states. By treating the measurement process as a stochastic dynamical map acting on the Bloch sphere for two-level systems and on the complex projective space CP^(N−1) for N-level systems, we derive explicit forms of f(G) that depend on the sectional curvature and the Fubini–Study metric. The resulting theory predicts that states situated in highly curved regions of the state space will exhibit accelerated decoherence compared to states in flatter regions. This geometric damping mechanism offers a novel perspective on the measurement problem and suggests new strategies for protecting quantum coherence by engineering state-space geometry. The potential for a Nobel Prize arises from the fundamental shift in understanding that geometry, rather than only dynamics, can control quantum measurement outcomes.