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Search Results (384)

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Keywords = entanglement measure

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14 pages, 465 KiB  
Article
Quantum W-Type Entanglement in Photonic Systems with Environmental Decoherence
by Kamal Berrada and Smail Bougouffa
Symmetry 2025, 17(7), 1147; https://doi.org/10.3390/sym17071147 - 18 Jul 2025
Viewed by 293
Abstract
Preserving quantum entanglement in multipartite systems under environmental decoherence is a critical challenge for quantum information processing. In this work, we investigate the dynamics of W-type entanglement in a system of three photons, focusing on the effects of Markovian and non-Markovian decoherence regimes. [...] Read more.
Preserving quantum entanglement in multipartite systems under environmental decoherence is a critical challenge for quantum information processing. In this work, we investigate the dynamics of W-type entanglement in a system of three photons, focusing on the effects of Markovian and non-Markovian decoherence regimes. Using the lower bound of concurrence (LBC) as a measure of entanglement, we analyze the time evolution of the LBC for photons initially prepared in a W state under the influence of dephasing noise. We explore the dependence of entanglement dynamics on system parameters such as the dephasing angle and refractive-index difference, alongside environmental spectral properties. Our results, obtained within experimentally feasible parameter ranges, reveal how the enhancement of entanglement preservation can be achieved in Markovian and non-Markovian regimes according to the system parameters. These findings provide valuable insights into the robustness of W-state entanglement in tripartite photonic systems and offer practical guidance for optimizing quantum protocols in noisy environments. Full article
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34 pages, 1302 KiB  
Article
Integrated Information in Relational Quantum Dynamics (RQD)
by Arash Zaghi
Appl. Sci. 2025, 15(13), 7521; https://doi.org/10.3390/app15137521 - 4 Jul 2025
Viewed by 308
Abstract
We introduce a quantum integrated-information measure Φ for multipartite states within the Relational Quantum Dynamics (RQD) framework. Φ(ρ) is defined as the minimum quantum Jensen–Shannon distance between an n-partite density operator ρ and any product state over a bipartition of [...] Read more.
We introduce a quantum integrated-information measure Φ for multipartite states within the Relational Quantum Dynamics (RQD) framework. Φ(ρ) is defined as the minimum quantum Jensen–Shannon distance between an n-partite density operator ρ and any product state over a bipartition of its subsystems. We prove that its square root induces a genuine metric on state space and that Φ is monotonic under all completely positive trace-preserving maps. Restricting the search to bipartitions yields a unique optimal split and a unique closest product state. From this geometric picture, we derive a canonical entanglement witness directly tied to Φ and construct an integration dendrogram that reveals the full hierarchical correlation structure of ρ. We further show that there always exists an “optimal observer”—a channel or basis—that preserves Φ better than any alternative. Finally, we propose a quantum Markov blanket theorem: the boundary of the optimal bipartition isolates subsystems most effectively. Our framework unites categorical enrichment, convex-geometric methods, and operational tools, forging a concrete bridge between integrated information theory and quantum information science. Full article
(This article belongs to the Special Issue Quantum Communication and Quantum Information)
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17 pages, 489 KiB  
Review
Experimental Advances in Phase Estimation with Photonic Quantum States
by Laura T. Knoll, Agustina G. Magnoni and Miguel A. Larotonda
Entropy 2025, 27(7), 712; https://doi.org/10.3390/e27070712 - 1 Jul 2025
Viewed by 694
Abstract
Photonic quantum metrology has emerged as a leading platform for quantum-enhanced precision measurements. By taking advantage of quantum resources such as entanglement, quantum metrology enables parameter estimation with sensitivities surpassing classical limits. In this review, we describe the basic tools and recent experimental [...] Read more.
Photonic quantum metrology has emerged as a leading platform for quantum-enhanced precision measurements. By taking advantage of quantum resources such as entanglement, quantum metrology enables parameter estimation with sensitivities surpassing classical limits. In this review, we describe the basic tools and recent experimental progress in the determination of an optical phase with a precision that may exceed the shot-noise limit, enabled by the use of nonclassical states of light. We review the state of the art and discuss the challenges and trends in the field. Full article
(This article belongs to the Section Quantum Information)
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30 pages, 479 KiB  
Review
Comprehensive Review of Metrics and Measurements of Quantum Systems
by Hassan Soubra, Hatem Elsayed, Yousef Elbrolosy, Youssef Adel and Zeyad Attia
Metrics 2025, 2(2), 9; https://doi.org/10.3390/metrics2020009 - 19 Jun 2025
Viewed by 702
Abstract
Quantum computing promises to offer significant computational advantages over classical computing, leveraging principles such as superposition and entanglement. This necessitates effective metrics and measurement techniques for evaluating quantum systems, aiding in their development and performance optimization. However, due to fundamental differences in computing [...] Read more.
Quantum computing promises to offer significant computational advantages over classical computing, leveraging principles such as superposition and entanglement. This necessitates effective metrics and measurement techniques for evaluating quantum systems, aiding in their development and performance optimization. However, due to fundamental differences in computing paradigms and current immaturity of quantum software abstractions, classical software and hardware metrics may not directly apply to quantum computing, where the distinction between software and hardware can still be somewhat indiscernible compared to classical computing. This paper provides a comprehensive review of existing quantum software and hardware metrics in the scientific literature, highlighting key challenges in the field. Additionally, it investigates the application of Functional Size Measurement (FSM), based on the COSMIC ISO 19761 FSM Method, to measure quantum software. Three FSM approaches are analyzed by applying them to Shor’s and Grover’s algorithms, with measurement results compared to assess their effectiveness. A comparative analysis highlights the strengths and limitations of each approach, emphasizing the need for further refinement. The insights from this study contribute to the advancement of quantum metrics, especially software metrics and measurement, paving the way for the development of a unified and standardized approach to quantum software measurement and assessment. Full article
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14 pages, 1641 KiB  
Article
Measurement-Induced Dynamical Quantum Thermalization
by Marvin Lenk, Sayak Biswas, Anna Posazhennikova and Johann Kroha
Entropy 2025, 27(6), 636; https://doi.org/10.3390/e27060636 - 14 Jun 2025
Viewed by 428
Abstract
One of the fundamental problems of quantum statistical physics is how an ideally isolated quantum system can ever reach thermal equilibrium behavior despite the unitary time evolution of quantum-mechanical systems. Here, we study, via explicit time evolution for the generic model system of [...] Read more.
One of the fundamental problems of quantum statistical physics is how an ideally isolated quantum system can ever reach thermal equilibrium behavior despite the unitary time evolution of quantum-mechanical systems. Here, we study, via explicit time evolution for the generic model system of an interacting, trapped Bose gas with discrete single-particle levels, how the measurement of one or more observables subdivides the system into observed and non-observed Hilbert subspaces and the tracing over the non-measured quantum numbers defines an effective, thermodynamic bath, induces the entanglement of the observed Hilbert subspace with the bath, and leads to a bi-exponential approach of the entanglement entropy and of the measured observables to thermal equilibrium behavior as a function of time. We find this to be more generally fulfilled than in the scenario of the eigenstate thermalization hypothesis (ETH), namely for both local particle occupation numbers and non-local density correlation functions, and independent of the specific initial quantum state of the time evolution. Full article
(This article belongs to the Special Issue Non-Equilibrium Dynamics in Ultra-Cold Quantum Gases)
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16 pages, 770 KiB  
Article
The Quantum Measurement Problem
by Erik B. Karlsson
Quantum Rep. 2025, 7(2), 28; https://doi.org/10.3390/quantum7020028 - 13 Jun 2025
Viewed by 1360
Abstract
Measurements play a specific role in quantum mechanics; only measurements allow us to catch a glimpse of the eluding physical reality. However, there is something deeply unsatisfactory with this specificity—a measurement is itself a physical process! Several varying modes of coping with this [...] Read more.
Measurements play a specific role in quantum mechanics; only measurements allow us to catch a glimpse of the eluding physical reality. However, there is something deeply unsatisfactory with this specificity—a measurement is itself a physical process! Several varying modes of coping with this dilemma have been proposed and this article tries to describe how a now-century-long discussion has led to new insights about the transition from the quantum to the classical world. Starting from the pioneer’s view of the quantum measurement problem, it follows the development of formalisms, the interest from philosophers for its new aspects on reality and how different interpretations of quantum mechanics have tried to support our classically working brains in understanding quantum phenomena. Decoherence is a main topic and its role in measurement processes exemplified. The question of whether the quantum measurement problem is now solved is left open for the readers’ own judgment. Full article
(This article belongs to the Special Issue 100 Years of Quantum Mechanics)
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22 pages, 3526 KiB  
Article
Indirect Regulation of SOC by Different Land Uses in Karst Areas Through the Modulation of Soil Microbiomes and Aggregate Stability
by Haiyuan Shu, Xiaoling Liang, Lei Hou, Meiting Li, Long Zhang, Wei Zhang and Yali Song
Agriculture 2025, 15(11), 1220; https://doi.org/10.3390/agriculture15111220 - 3 Jun 2025
Viewed by 458
Abstract
Natural restoration of vegetation and plantation are effective land use measures to promote soil organic carbon (SOC) sequestration. How soil physicochemical properties, microorganisms, Glomalin-related soil proteins (GRSPs), and aggregates interact to regulate SOC accumulation and sequestration remains unclear. This study examined five land [...] Read more.
Natural restoration of vegetation and plantation are effective land use measures to promote soil organic carbon (SOC) sequestration. How soil physicochemical properties, microorganisms, Glomalin-related soil proteins (GRSPs), and aggregates interact to regulate SOC accumulation and sequestration remains unclear. This study examined five land uses in the karst region of Southwest China: corn field (CF), corn intercropped with cabbage fields (CICF), orchard (OR), plantation (PL), and natural restoration of vegetation (NRV). The results revealed that SOC, total nitrogen (TN), total phosphorus (TP), total GRSP (T-GRSP), and easily extractable GRSP (EE-GRSP) contents were significantly higher under NRV and PL than in the CF, CICF, and OR, with increases ranging from 10.69% to 266.72%. Land use significantly influenced bacterial α-diversity, though fungal α-diversity remained unaffected. The stability of soil aggregates among the five land uses followed the order: PL > NRV > CF > OR > CICF. Partial least-squares path modeling (PLS-PM) identified land use as the most critical factor influencing SOC. SOC accumulation and stability were enhanced through improved soil properties, increased microbial diversity, and greater community abundance, promoting GRSP secretion and strengthening soil aggregate stability. In particular, soil microorganisms adhere to the aggregates of soil particles through the entanglement of fine roots and microbial hyphae and their secretions (GRSPs, etc.) to maintain the stability of the aggregates, thus protecting SOC from decomposition. Natural restoration of vegetation and plantation proved more effective for soil carbon sequestration in the karst region of Southwest China compared to sloping cropland and orchards. Full article
(This article belongs to the Section Agricultural Soils)
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23 pages, 1563 KiB  
Article
The Proposal of a Fully Quantum Neural Network and Fidelity-Driven Training Using Directional Gradients for Multi-Class Classification
by Dawid Ewald
Electronics 2025, 14(11), 2189; https://doi.org/10.3390/electronics14112189 - 28 May 2025
Viewed by 561
Abstract
In this work, we present a training method for a Fully Quantum Neural Network (FQNN) based entirely on quantum circuits. The model processes data exclusively through quantum operations, without incorporating classical neural network layers. In the proposed architecture, the roles of classical neurons [...] Read more.
In this work, we present a training method for a Fully Quantum Neural Network (FQNN) based entirely on quantum circuits. The model processes data exclusively through quantum operations, without incorporating classical neural network layers. In the proposed architecture, the roles of classical neurons and weights are assumed, respectively, by qubits and parameterized quantum gates: input features are encoded into quantum states of qubits, while the network weights correspond to the rotation angles of quantum gates that govern the system’s state evolution. The optimization of gate parameters is performed using directional gradient estimation, where gradients are numerically approximated via finite differences, eliminating the need for analytic derivation. The training objective is defined as the quantum-state fidelity, which measures the similarity between the network’s output state and a reference state representing the correct class. Experiments were conducted using the Qiskit AerSimulator, which allows for the accurate simulation of quantum circuits on a classical computer. The proposed approach was applied to the classification of the Iris dataset. The experimental results demonstrate that the FQNN is capable of effectively learning to distinguish between classes based on input features, achieving stable test accuracy across runs. These findings confirm the feasibility of constructing fully quantum classifiers without relying on hybrid quantum—classical architectures. The FQNN architecture consists of multiple quantum layers, each incorporating parameterized rotation operations and entanglement between qubits. The number of layers is determined by the ratio of quantum parameters (weights) to the number of input features. Each layer functions analogously to a hidden layer in a classical neural network, transforming the quantum-state space into a richer feature representation through controlled quantum operations. As a result, the network is capable of dynamically modeling dependencies among input features without the use of classical activation functions. Full article
(This article belongs to the Section Artificial Intelligence)
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12 pages, 1589 KiB  
Article
Single-State Multi-Party Quantum Key Agreement with Single-Particle Measurement
by Hao Yang, Dunbo Cai, Ling Qian, Runqing Zhang, Songfeng Lu and Chengfu Sun
Entropy 2025, 27(4), 405; https://doi.org/10.3390/e27040405 - 10 Apr 2025
Viewed by 322
Abstract
In this study, we propose a single-state multi-party quantum key agreement (MQKA) protocol with single-particle measurement. Firstly, a single-state three-party quantum key agreement protocol with single-particle measurement is introduced, followed by a security analysis that validated its capability to resist potential internal and [...] Read more.
In this study, we propose a single-state multi-party quantum key agreement (MQKA) protocol with single-particle measurement. Firstly, a single-state three-party quantum key agreement protocol with single-particle measurement is introduced, followed by a security analysis that validated its capability to resist potential internal and external attacks. Furthermore, we utilize multi-particle entangled states to present a multi-party version of the single-state multi-party quantum key agreement with single-particle measurement. In comparison to previous MQKA protocols, our approach presents the following advantages: it employs one kind of multi-particle entangled state as the quantum resource; eliminates the need for entanglement swapping techniques, unitary operations, or pre-shared keys between participants; uses only the X measurement basis and Z measurement basis; transmits fewer qubits; consumes fewer qubits; and has higher qubit efficiency. Full article
(This article belongs to the Section Quantum Information)
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11 pages, 475 KiB  
Article
Stability of Bi-Partite Correlations in Symmetric N-Qubit States Under Deterministic Measurements
by Carlos Muñoz, Luis Roa and Andrei B. Klimov
Physics 2025, 7(2), 12; https://doi.org/10.3390/physics7020012 - 9 Apr 2025
Viewed by 587
Abstract
In this paper, we analyze the distribution of bi-partite correlations in pure symmetric N-qubit states during local deterministic measurements, which ensure the same value of the reduced purities in the outcome states. It is analytically shown that all reduced purities grow in [...] Read more.
In this paper, we analyze the distribution of bi-partite correlations in pure symmetric N-qubit states during local deterministic measurements, which ensure the same value of the reduced purities in the outcome states. It is analytically shown that all reduced purities grow in the process of deterministic measurements. This allows us to characterize the stability of bi-partite entanglement during the optimal correlation transfer under single-qubit measurements in the asymptotic limit N1. Full article
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26 pages, 339 KiB  
Review
Quantum-Inspired Statistical Frameworks: Enhancing Traditional Methods with Quantum Principles
by Theodoros Kyriazos and Mary Poga
Encyclopedia 2025, 5(2), 48; https://doi.org/10.3390/encyclopedia5020048 - 4 Apr 2025
Cited by 1 | Viewed by 1312
Abstract
This manuscript introduces a comprehensive framework for augmenting classical statistical methodologies through the targeted integration of core quantum mechanical principles—specifically superposition, entanglement, measurement, wavefunctions, and density matrices. By concentrating on these foundational concepts instead of the whole expanse of quantum theory, we propose [...] Read more.
This manuscript introduces a comprehensive framework for augmenting classical statistical methodologies through the targeted integration of core quantum mechanical principles—specifically superposition, entanglement, measurement, wavefunctions, and density matrices. By concentrating on these foundational concepts instead of the whole expanse of quantum theory, we propose “quantum-inspired” models that address persistent shortcomings in conventional statistical approaches. In particular, five pivotal distributions (normal, binomial, Poisson, Student’s t, and chi-square) are reformulated to incorporate interference terms, phase factors, and operator-based transformations, thereby facilitating the representation of multimodal data, phase-sensitive dependencies, and correlated event patterns—characteristics that are frequently underrepresented in purely real-valued, classical frameworks. Furthermore, ten quantum-inspired statistical principles are delineated to guide practitioners in systematically adapting quantum mechanics for traditional inferential tasks. These principles are illustrated through domain-specific applications in finance, cryptography (distinct from direct quantum cryptography applications), healthcare, and climate modeling, demonstrating how amplitude-based confidence measures, density matrices, and measurement analogies can enrich standard statistical models by capturing more nuanced correlation structures and enhancing predictive performance. By unifying quantum constructs with established statistical theory, this work underscores the potential for interdisciplinary collaboration and paves the way for advanced data analysis tools capable of addressing high-dimensional, complex, and dynamically evolving datasets. Complete R code ensures reproducibility and further exploration. Full article
(This article belongs to the Section Mathematics & Computer Science)
14 pages, 254 KiB  
Article
Multiparty Quantum Private Comparison Using Rotation Operations
by Min Hou and Yue Wu
Axioms 2025, 14(4), 274; https://doi.org/10.3390/axioms14040274 - 3 Apr 2025
Cited by 1 | Viewed by 333
Abstract
This paper presents a multiparty quantum private comparison (MQPC) protocol that facilitates multiple users to compare the equality of their private inputs while preserving the confidentiality of each input through the principles of quantum mechanics. In our approach, users initially convert their secret [...] Read more.
This paper presents a multiparty quantum private comparison (MQPC) protocol that facilitates multiple users to compare the equality of their private inputs while preserving the confidentiality of each input through the principles of quantum mechanics. In our approach, users initially convert their secret integers into binary representations, which are then encoded into single photons that act as carriers of the information. These encoded single-photon states undergo encryption via rotational operations, effectively obscuring the original inputs before transmission to a semi-honest third party (TP). The TP decrypts the quantum states and conducts Z-basis measurements to derive the comparison results. To enhance security, the protocol incorporates decoy photons, enabling participants to detect potential eavesdropping on the quantum channel. Importantly, even if the TP or other participants attempt to glean insights into each other’s inputs, the encryption via rotational operations ensures that private information remains inaccessible. This protocol demonstrates significant advancements in practicality compared to existing MQPC frameworks that rely on complex quantum technologies, such as entanglement swapping and multi-particle entanglement. By leveraging the simplicity of single photons, rotation operations, and Z-basis measurements, our protocol is more accessible for implementation. Full article
(This article belongs to the Section Mathematical Physics)
20 pages, 1343 KiB  
Article
Loop-Back Quantum Key Distribution (QKD) for Secure and Scalable Multi-Node Quantum Networks
by Luis Adrián Lizama-Perez and J. M. López-Romero
Symmetry 2025, 17(4), 521; https://doi.org/10.3390/sym17040521 - 30 Mar 2025
Viewed by 833
Abstract
Quantum key distribution (QKD) is a cornerstone of secure communication in the quantum era, yet most existing protocols are designed for point-to-point transmission, limiting their scalability in networked environments. In this work, we introduce Loop-Back QKD, a novel QKD protocol that supports both [...] Read more.
Quantum key distribution (QKD) is a cornerstone of secure communication in the quantum era, yet most existing protocols are designed for point-to-point transmission, limiting their scalability in networked environments. In this work, we introduce Loop-Back QKD, a novel QKD protocol that supports both two-party linear configurations and scalable multiuser ring topologies. By leveraging a structured turn-based mechanism and bidirectional pulse propagation, the protocol enables efficient key distribution while reducing the quantum bit error rate (QBER) through a multi-pulse approach. Unlike trusted-node QKD networks, Loop-Back QKD eliminates intermediate-node vulnerabilities, as secret keys are never processed by intermediate nodes. Furthermore, unlike Measurement-Device-Independent (MDI-QKD) and Twin-Field QKD (TF-QKD), which require complex entanglement-based setups, Loop-Back QKD relies solely on direct polarization transformations, reducing vulnerability to side-channel attacks and practical implementation challenges. Additionally, our analysis indicates that multi-pulse Loop-Back QKD can tolerate higher QBER thresholds. However, this increased robustness comes at the cost of a lower key rate efficiency compared to standard QKD schemes. This design choice enhances its robustness against real-world adversarial threats, making it a strong candidate for secure multiuser communication in local and metropolitan-scale quantum networks. Full article
(This article belongs to the Section Computer)
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12 pages, 1236 KiB  
Article
Protecting the Entanglement of X-Type Systems via Weak Measurement and Reversal in the Generalized Amplitude Damping Channel
by Meijiao Wang, Haojie Liu, Lianzhen Cao, Yang Yang, Xia Liu, Bing Sun and Jiaqiang Zhao
Entropy 2025, 27(4), 350; https://doi.org/10.3390/e27040350 - 27 Mar 2025
Cited by 1 | Viewed by 497
Abstract
The study of system evolution in generalized amplitude damping is of great significance in quantum information science and quantum computing. As an important quantum noise channel, the generalized amplitude damping channel can describe the general phenomenon of the energy dissipation effect in quantum [...] Read more.
The study of system evolution in generalized amplitude damping is of great significance in quantum information science and quantum computing. As an important quantum noise channel, the generalized amplitude damping channel can describe the general phenomenon of the energy dissipation effect in quantum systems at finite temperature. In this paper, we study the use of weak measurement and reversal to protect the entanglement of X-type systems in generalized amplitude damping channels, and give an experimental scheme. The results show that the closer to zero the temperature environment, the better the protection effect of weak measurement and reversal, but the lower the success rate. Therefore, when choosing an experimental environment, it is important to consider not only the temperature factor but also the probability of success. Because all quantum systems work at finite temperatures, it is hoped that the study of generalized amplitude damping channels can help design more robust quantum algorithms and protocols to improve the efficiency and stability of quantum information processing. Full article
(This article belongs to the Special Issue Quantum Entanglement—Second Edition)
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13 pages, 3021 KiB  
Article
Finite Element Modeling of Acoustic Nonlinearity Derived from Plastic Deformation of 35CrMoA Steel
by Shumin Yu, Lei Hu, Xingbin Yang and Xiangyu Ji
Metals 2025, 15(4), 343; https://doi.org/10.3390/met15040343 - 21 Mar 2025
Viewed by 329
Abstract
Acoustic nonlinearity derived from microstructural evolution of metallic materials during plastic deformation has been found to be a promising nondestructive technique to identify early stage plastic damage in metallic structural components. In the current investigation, the propagation of longitudinal ultrasonic waves in plastically [...] Read more.
Acoustic nonlinearity derived from microstructural evolution of metallic materials during plastic deformation has been found to be a promising nondestructive technique to identify early stage plastic damage in metallic structural components. In the current investigation, the propagation of longitudinal ultrasonic waves in plastically deformed 35CrMoA steel plates was simulated using finite element (FE) methods based on the theory of dislocation-induced acoustic nonlinearity to establish the relationship between acoustic nonlinearity parameters and plastic strain. Experiments were conducted to validate the numerical model. Both simulated and experimental results demonstrate a monotonic increase in the acoustic nonlinearity parameter with applied plastic strain. The simulated ultrasonic nonlinear parameters deviate from experimental measurements in a two-stage pattern. In the low-strain regime (plastic strain < 8.5%), FE predictions underestimate experimental values, possibly due to dislocation entanglement in high-density regions that restricts dislocation mobility and suppresses acoustic nonlinearity. The FE model overestimates the parameters when plastic strain exceeds about 8.5%. This reversal is related to the formation of dislocation cells and walls with enhanced acoustic nonlinearity. Full article
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