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Scientific Reports

Coherence lengths and quantum entanglement in radiative capture reactions

Mehdi Mirzaee, Hossein Sadeghi

Published May 12, 2025• 3 citations
Publisher

Abstract

Coherence length ([Formula: see text]) is a key concept in quantum mechanics, representing the ability of a quantum system to maintain well-defined phase relationships over time. This paper investigates the relationship between coherence length, decay width (Γ), and atomic mass in radiative capture reactions using a machine learning model. Additionally, the quantum entanglement of the resulting states is quantified using the von Neumann entropy. The results demonstrate the inverse relationship between coherence length and decay width, highlighting the universal nature of this relationship across various reactions. The findings provide valuable insights into the behavior of particles in radiative capture reactions and have implications for both experimental and theoretical studies in nuclear and particle physics.

DOI
10.1038/s41598-025-01433-0

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Coherence length ([Formula: see text]) is a key concept in quantum mechanics, representing the ability of a quantum system to maintain well-defined phase relationships over time. This paper investigates the relationship between coherence length, decay width (Γ), and atomic mass in radiative capture reactions using a machine learning model. Additionally, the quantum entanglement of the resulting states is quantified using the von Neumann entropy. The results demonstrate the inverse relationship between coherence length and decay width, highlighting the universal nature of this relationship across various reactions. The findings provide valuable insights into the behavior of particles in radiative capture reactions and have implications for both experimental and theoretical studies in nuclear and particle physics.
This paper presents a comprehensive investigation of quantum correlations in radiative-capture reactions through a unified lens of quantum information theory and nuclear physics. By combining density matrix formulations with open quantum system dynamics, we can establish universal scaling laws governing the relationship between quantum discord (D), entanglement entropy (S), and fundamental nuclear properties. The analysis reveals the inverse power-law dependencies [Formula: see text] and [Formula: see text] between these quantum metrics and the decay width (Γ), maintained across fourteen nuclear systems spanning six decades in Γ and masses [Formula: see text]. A machine learning architecture that integrates physical constraints with deep residual networks achieves 92% prediction accuracy for coherence lengths [Formula: see text] while identifying shell structure effects that enhance quantum correlations near magic numbers. The persistent quantum discord ([Formula: see text]) observed in systems with sub-attometer coherence lengths suggests nuclear spins maintain non-classical correlations through internal degrees of freedom rather than spatial coherence. The developed phase diagram categorizes nuclear reactions into three quantum technology regimes: memory ([Formula: see text] s[Formula: see text]), sensing ([Formula: see text] s[Formula: see text]), and foundational tests ([Formula: see text] s[Formula: see text]), with [Formula: see text]Fe[Formula: see text] and [Formula: see text]Li[Formula: see text] identified as optimal candidates for applications. These results bridge nuclear physics with quantum information science, providing both theoretical insights into decoherence mechanisms and practical tools for quantum material design. The proposed methodology establishes radiative capture reactions as a novel platform for exploring emergent quantum phenomena in strongly interacting systems.
Quantum entanglement represents a fundamental resource for quantum information processing, yet the dynamics of multi-photon entangled systems remain inadequately characterized for practical quantum computing applications. This research investigates the generation, manipulation, and characterization of entangled states involving two to eight photons using spontaneous parametric down-conversion techniques. Through theoretical analysis and numerical simulations, we developed a comprehensive framework that quantifies entanglement fidelity, decoherence rates, and Bell inequality violations across various multi-photon configurations. Our findings reveal that entanglement fidelity decreases exponentially with increasing photon number, exhibiting a decay constant of 0.087±0.012 per additional qubit in optical systems. The research demonstrates significant variations in decoherence times across different physical implementations, with ion trap systems maintaining coherence 1.7 times longer than photonic platforms for equivalent qubit numbers. We established mathematical relationships between system parameters and entanglement quality metrics, identifying critical thresholds for fault-tolerant quantum gate operations. The theoretical framework incorporates realistic noise models, environmental coupling mechanisms, and measurement-induced perturbations that affect practical implementations. Our analysis indicates that five-photon entangled states maintain sufficient fidelity (>83.5%) for error-corrected quantum algorithms when decoherence times exceed 75 microseconds. These results provide essential guidelines for designing scalable quantum processors and establishing benchmarks for experimental validation of multi-qubit entanglement protocols.
This paper explores the fundamental relationship between the geometry of entanglement and von Neumann entropy, shedding light on the intricate nature of quantum correlations. We provide a comprehensive overview of entanglement, highlighting its crucial role in quantum mechanics. Our focus centers on the connection between entanglement, von Neumann entropy, a measure of the information content within quantum systems and the geometry of composite Hilbert spaces. We discuss various methods for quantifying and characterizing entanglement through a geometric perspective and elucidate how this connection unveils the nature of quantum entanglement, offering valuable insights into the underlying structure of quantum systems. This study underscores the significance of geometry as a key tool for understanding the rich landscape of quantum correlations and their implications across various domains of physics and information theory. An example of entanglement as an indispensable resource for the task of state teleportation is presented at the end.
The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with multiple approaches having varying interpretations and levels of computability and measurability. Here, we introduce two measures that capture independent macroscopic properties: i) extensive size, measuring the degree of coherence in position or momentum observables relative to atomic-scale units, and ii) entangled size, quantifying the number of entangled subsystems. These measures unify many desirable features of past proposals while having rigorously justified interpretations from quantum information theory in terms of coherence and multipartite entanglement. We demonstrate how to estimate them and obtain lower-bounds using experimental data from micro-mechanical oscillators and diffracting molecules. Notably, we find evidence for genuine multipartite entanglement of 10 5 to 10 7 atoms in recent mechanical superposition states.
Quantum entanglement, a fundamental phenomenon of quantum mechanics, is increasingly recognized for its potential role in governing the behavior of chemical systems and reactions. While theoretical predictions suggest entanglement can influence reaction pathways, rates, and product distributions, its direct detection and characterization in complex molecular environments remain significant challenges due to the inherent complexity and decoherence effects. This paper proposes a novel framework utilizing machine learning techniques to identify and interpret quantum entanglement signatures embedded within the high-dimensional data generated by quantum chemical reaction dynamics simulations. We outline a methodology that involves generating comprehensive datasets of molecular trajectories and quantum observables for various chemical reactions, followed by the application of advanced machine learning models, including deep neural networks, to discern subtle patterns indicative of entanglement. The approach aims to extract chemically intuitive features correlating with entanglement measures, thereby providing a powerful tool for understanding the role of quantum mechanics beyond classical approximations in chemical transformations. This work not only seeks to advance the fundamental understanding of quantum entanglement in chemistry but also paves the way for the design of quantum-informed chemical reactions and materials with tailored properties.
Entanglement entropy is a fundamental measure of quantum correlations and a key resource underpinning advances in quantum information and many-body physics. We uncover a universal relationship between bipartite entanglement entropy and particle number after the barrier in a one-dimensional Fermi-Hubbard system with an external asymmetric potential. Decomposing the von Neumann entropy into number entropy S n and configurational entropy S c , we show that in the barrier-dominated tunneling regime both components are individually well-defined functions of the postbarrier particle density n A , even though S c encodes off-diagonal coherences that are not directly accessible from density measurements alone. Using Kolmogorov-Arnold networks—a novel machine learning architecture—we learn the relationship for entropy and its components across a broad range of interaction strengths and barrier heights with high predictive accuracy. Furthermore, we propose a simple analytical binary-entropy-like expression that quantitatively captures the observed correlation for fixed parameters. Our findings open avenues for characterizing quantum correlations in transport phenomena and provide a powerful framework for estimating the full von Neumann entropy—including its configurational component—from a single transport observable.