Entropy

18 pages, 6818 KiB

Open AccessArticle

Deep Learning-Based Min-Entropy-Accelerated Evaluation for High-Speed Quantum Random Number Generation

by Xiaomin Guo, Wenhe Zhou, Yue Luo, Xiangyu Meng, Jiamin Li, Yaoxing Bian, Yanqiang Guo and Liantuan Xiao

Entropy 2025, 27(8), 786; https://doi.org/10.3390/e27080786 - 24 Jul 2025

Abstract

Secure communication is critically dependent on high-speed and high-security quantum random number generation (QRNG). In this work, we present a responsive approach to enhance the efficiency and security of QRNG by leveraging polarization-controlled heterodyne detection to simultaneously measure the quadrature amplitude and phase [...] Read more.

Secure communication is critically dependent on high-speed and high-security quantum random number generation (QRNG). In this work, we present a responsive approach to enhance the efficiency and security of QRNG by leveraging polarization-controlled heterodyne detection to simultaneously measure the quadrature amplitude and phase fluctuations of vacuum shot noise. To address the practical non-idealities inherent in QRNG systems, we investigate the critical impacts of imbalanced heterodyne detection, amplitude–phase overlap, finite-size effects, and security parameters on quantum conditional min-entropy derived from the entropy uncertainty principle. It effectively mitigates the overestimation of randomness and fortifies the system against potential eavesdropping attacks. For a high-security parameter of

10^{- 20}

, QRNG achieves a true random bit extraction ratio of 83.16% with a corresponding real-time speed of 37.25 Gbps following a 16-bit analog-to-digital converter quantization and 1.4 GHz bandwidth extraction. Furthermore, we develop a deep convolutional neural network for rapid and accurate entropy evaluation. The entropy evaluation of 13,473 sets of quadrature data is processed in 68.89 s with a mean absolute percentage error of 0.004, achieving an acceleration of two orders of magnitude in evaluation speed. Extracting the shot noise with full detection bandwidth, the generation rate of QRNG using dual-quadrature heterodyne detection exceeds 85 Gbps. The research contributes to advancing the practical deployment of QRNG and expediting rapid entropy assessment. Full article

(This article belongs to the Section Quantum Information)

25 pages, 27206 KiB

Open AccessArticle

KCUNET: Multi-Focus Image Fusion via the Parallel Integration of KAN and Convolutional Layers

by Jing Fang, Ruxian Wang, Xinglin Ning, Ruiqing Wang, Shuyun Teng, Xuran Liu, Zhipeng Zhang, Wenfeng Lu, Shaohai Hu and Jingjing Wang

Entropy 2025, 27(8), 785; https://doi.org/10.3390/e27080785 - 24 Jul 2025

Abstract

Multi-focus image fusion (MFIF) is an image-processing method that aims to generate fully focused images by integrating source images from different focal planes. However, the defocus spread effect (DSE) often leads to blurred or jagged focus/defocus boundaries in fused images, which affects the [...] Read more.

Multi-focus image fusion (MFIF) is an image-processing method that aims to generate fully focused images by integrating source images from different focal planes. However, the defocus spread effect (DSE) often leads to blurred or jagged focus/defocus boundaries in fused images, which affects the quality of the image. To address this issue, this paper proposes a novel model that embeds the Kolmogorov–Arnold network with convolutional layers in parallel within the U-Net architecture (KCUNet). This model keeps the spatial dimensions of the feature map constant to maintain high-resolution details while progressively increasing the number of channels to capture multi-level features at the encoding stage. In addition, KCUNet incorporates a content-guided attention mechanism to enhance edge information processing, which is crucial for DSE reduction and edge preservation. The model’s performance is optimized through a hybrid loss function that evaluates in several aspects, including edge alignment, mask prediction, and image quality. Finally, comparative evaluations against 15 state-of-the-art methods demonstrate KCUNet’s superior performance in both qualitative and quantitative analyses. Full article

(This article belongs to the Section Signal and Data Analysis)

25 pages, 543 KiB

Open AccessArticle

CurveMark: Detecting AI-Generated Text via Probabilistic Curvature and Dynamic Semantic Watermarking

by Yuhan Zhang, Xingxiang Jiang, Hua Sun, Yao Zhang and Deyu Tong

Entropy 2025, 27(8), 784; https://doi.org/10.3390/e27080784 - 24 Jul 2025

Abstract

Large language models (LLMs) pose significant challenges to content authentication, as their sophisticated generation capabilities make distinguishing AI-produced text from human writing increasingly difficult. Current detection methods suffer from limited information capture, poor rate–distortion trade-offs, and vulnerability to adversarial perturbations. We present CurveMark, [...] Read more.

Large language models (LLMs) pose significant challenges to content authentication, as their sophisticated generation capabilities make distinguishing AI-produced text from human writing increasingly difficult. Current detection methods suffer from limited information capture, poor rate–distortion trade-offs, and vulnerability to adversarial perturbations. We present CurveMark, a novel dual-channel detection framework that combines probability curvature analysis with dynamic semantic watermarking, grounded in information-theoretic principles to maximize mutual information between text sources and observable features. To address the limitation of requiring prior knowledge of source models, we incorporate a Bayesian multi-hypothesis detection framework for statistical inference without prior assumptions. Our approach embeds imperceptible watermarks during generation via entropy-aware, semantically informed token selection and extracts complementary features from probability curvature patterns and watermark-specific metrics. Evaluation across multiple datasets and LLM architectures demonstrates 95.4% detection accuracy with minimal quality degradation (perplexity increase < 1.3), achieving 85–89% channel capacity utilization and robust performance under adversarial perturbations (72–94% information retention). Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

22 pages, 887 KiB

Open AccessArticle

Influences of Language Functions on Linguistic Features: Multi-Dimensional and Entropy Analyses of Academic and Entertainment Registers

by Changwei Hu, Yu Zhu and Liangjie Yuan

Entropy 2025, 27(8), 783; https://doi.org/10.3390/e27080783 - 24 Jul 2025

Abstract

This study examines how language functions impact linguistic features in academic and entertainment registers. Using multi-dimensional analysis (MDA) and computing entropy values, we analyze a large-scale Chinese corpus consisting of over 19 million tokens from 1000 texts, including academic journals, dissertations, entertainment magazines, [...] Read more.

This study examines how language functions impact linguistic features in academic and entertainment registers. Using multi-dimensional analysis (MDA) and computing entropy values, we analyze a large-scale Chinese corpus consisting of over 19 million tokens from 1000 texts, including academic journals, dissertations, entertainment magazines, and novellas. We identify key language functions that shape linguistic features within these registers. Our results reveal five core dimensions of linguistic functional variation, narrative versus rational discourse, modification, reference, uncertainty, and prudence, which account for over 52% of the variance in language use. Certain linguistic features systematically co-occur in each dimension, forming language functions that underpin broader social networks. Entropy values further confirm the findings of multi-dimensional analysis. This study emphasizes the associations between linguistic features and language functions, offering a theoretical perspective for understanding how language functions impact linguistic features and shape different registers. The findings suggest a language variation perspective on social networks’ communication. Full article

(This article belongs to the Special Issue Complexity of Social Networks)

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26 pages, 3959 KiB

Open AccessArticle

Fault Diagnosis Method of Planetary Gearboxes Based on Multi-Scale Wavelet Packet Energy Entropy and Extreme Learning Machine

by Rui Meng, Junpeng Zhang, Ming Chen and Liangliang Chen

Entropy 2025, 27(8), 782; https://doi.org/10.3390/e27080782 - 24 Jul 2025

Abstract

As critical components of planetary gearboxes, gears directly affect mechanical system reliability when faults occur. Traditional feature extraction methods exhibit limitations in accurately identifying fault characteristics and achieving satisfactory diagnostic accuracy. This research is concerned with the gear of the planetary gearbox and [...] Read more.

As critical components of planetary gearboxes, gears directly affect mechanical system reliability when faults occur. Traditional feature extraction methods exhibit limitations in accurately identifying fault characteristics and achieving satisfactory diagnostic accuracy. This research is concerned with the gear of the planetary gearbox and proposes a new approach termed multi-scale wavelet packet energy entropy (MSWPEE) for extracting gear fault features. The signal is split into sub-signals at three different scale factors. Following decomposition and reconstruction using the wavelet packet algorithm, the wavelet packet energy entropy for each node is computed under different operating conditions. A feature vector is formed by combining the wavelet packet energy entropy at different scale factors. Furthermore, this study proposes a method combining multi-scale wavelet packet energy entropy with extreme learning machine (MSWPEE-ELM). The experimental findings validate the precision of this approach in extracting features and diagnosing faults in sun gears with varying degrees of tooth breakage severity. Full article

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43 pages, 843 KiB

Open AccessArticle

A Missing Link: The Double-Slit Experiment and Quantum Entanglement

by Arkady Plotnitsky

Entropy 2025, 27(8), 781; https://doi.org/10.3390/e27080781 - 24 Jul 2025

Abstract

This article reconsiders the double-slit experiment by establishing a new type of relationship between it and the concept of entanglement. While the role of entanglement in the double-slit experiment has been considered, this particular relationship appears to have been missed in preceding discussions [...] Read more.

This article reconsiders the double-slit experiment by establishing a new type of relationship between it and the concept of entanglement. While the role of entanglement in the double-slit experiment has been considered, this particular relationship appears to have been missed in preceding discussions of the experiment, even by Bohr, who extensively used it to support his argument concerning quantum physics. The main reason for this relationship is the different roles of the diaphragm with slits in two setups, S1 and S2, defining the double-slit experiment as a quantum experiment. In S1, in each individual run of the experiment one can in principle (even if not actually) know throughout which slit the quantum object considered has passed; in S2 this knowledge is in principle impossible, which impossibility is coextensive with the appearance of the interference pattern, once a sufficient number of individual runs of the experiment have taken place. The article offers the following argument based on two new concepts, an “experimentally quantum object” and an “ontologically quantum object.” In S1 the diaphragm can be treated as part of an observational arrangement and thus considered as a classical object, while the object passing through one or the other slit is considered as an “ontologically quantum object,” defined as an object necessary to establish a quantum phenomenon. By contrast, in S2, the diaphragm can, via the concept of Heisenberg-von-Neumann cut, be treated as an “experimentally quantum object,” defined as an object treatable by quantum theory, even while possibly being an ontologically classical object. This interaction is not an observation but a quantum entanglement between these two quantum objects, one ontologically and one experimentally quantum. This argument is grounded in a particular interpretation of quantum phenomena and quantum theory, which belongs to the class of interpretations designated here as “reality without realism” (RWR) interpretations. The article also argues that wave-particle complementarity, with which the concept of complementarity is often associated, plays little, if any, role in quantum physics, or in Bohr’s thinking, and may be misleading in considering the double-slit experiment, often explained by using this complementarity. Full article

(This article belongs to the Special Issue Quantum Probability and Randomness V)

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23 pages, 594 KiB

Open AccessArticle

Information-Theoretic Cost–Benefit Analysis of Hybrid Decision Workflows in Finance

by Philip Beaucamp, Harvey Maylor and Min Chen

Entropy 2025, 27(8), 780; https://doi.org/10.3390/e27080780 - 23 Jul 2025

Abstract

Analyzing and leveraging data effectively has been an advantageous strategy in the management workflows of many contemporary organizations. In business and finance, data-informed decision workflows are nowadays essential for enabling development and growth. However, there is yet a theoretical or quantitative approach for [...] Read more.

Analyzing and leveraging data effectively has been an advantageous strategy in the management workflows of many contemporary organizations. In business and finance, data-informed decision workflows are nowadays essential for enabling development and growth. However, there is yet a theoretical or quantitative approach for analyzing the cost–benefit of the processes in such workflows, e.g., in determining the trade-offs between machine- and human-centric processes and quantifying biases. The aim of this work is to translate an information-theoretic concept and measure for cost–benefit analysis to a methodology that is relevant to the analysis of hybrid decision workflows in business and finance. We propose to combine an information-theoretic approach (i.e., information-theoretic cost–benefit analysis) and an engineering approach (e.g., workflow decomposition), which enables us to utilize information-theoretic measures to estimate the cost–benefit of individual processes quantitatively. We provide three case studies to demonstrate the feasibility of the proposed methodology, including (i) the use of a statistical and computational algorithm, (ii) incomplete information and humans’ soft knowledge, and (iii) cognitive biases in a committee meeting. While this is an early application of information-theoretic cost–benefit analysis to business and financial workflows, it is a significant step towards the development of a systematic, quantitative, and computer-assisted approach for optimizing data-informed decision workflows. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance and Management, 3rd Edition)

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26 pages, 412 KiB

Open AccessArticle

Entropy and Stability: Reduced Hamiltonian Formalism of Non-Barotropic Flows and Instability Constraints

by Asher Yahalom

Entropy 2025, 27(8), 779; https://doi.org/10.3390/e27080779 - 23 Jul 2025

Abstract

A reduced representation of a dynamical system helps us to understand what the true degrees of freedom of that system are and thus what the possible instabilities are. Here we extend previous work on barotropic flows to the more general non-barotropic flow case [...] Read more.

A reduced representation of a dynamical system helps us to understand what the true degrees of freedom of that system are and thus what the possible instabilities are. Here we extend previous work on barotropic flows to the more general non-barotropic flow case and study the implications for variational analysis and conserved quantities of topological significance such as circulation and helicity. In particular we introduce a four-function Eulerian variational principle of non-barotropic flows, which has not been described before. Also new conserved quantities of non-barotropic flows related to the topological velocity field, topological circulation and topological helicity, including a local version of topological helicity, are introduced. The variational formalism given in terms of a Lagrangian density allows us to introduce canonical momenta and hence a Hamiltonian formalism. Full article

(This article belongs to the Special Issue Unstable Hamiltonian Systems and Scattering Theory)

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14 pages, 541 KiB

Open AccessArticle

Joint Optimization and Performance Analysis of Analog Shannon–Kotel’nikov Mapping for OFDM with Carrier Frequency Offset

by Jingwen Lin, Qiwang Chen, Yu Hua and Chen Chen

Entropy 2025, 27(8), 778; https://doi.org/10.3390/e27080778 - 23 Jul 2025

Abstract

An analog joint source-channel coding (AJSCC) based on Shannon–Kotel’nikov (S-K) mapping transmitting discrete-time encoded samples in orthogonal frequency division multiplexing (OFDM) systems over wireless channel has exhibited excellent performance. However, the phenomenon of carrier frequency offset (CFO) caused by the frequency mismatch between [...] Read more.

An analog joint source-channel coding (AJSCC) based on Shannon–Kotel’nikov (S-K) mapping transmitting discrete-time encoded samples in orthogonal frequency division multiplexing (OFDM) systems over wireless channel has exhibited excellent performance. However, the phenomenon of carrier frequency offset (CFO) caused by the frequency mismatch between the transmitter’s and receiver’s local oscillators often exists in actual scenarios; thus, in this paper the performance of AJSCC-OFDM with CFO is analyzed and the S-K mapping is optimized. A joint optimization strategy is developed to maximize the signal-to-distortion ratio (SDR) subject to CFO constraints. Considering that the optimized AJSCC-OFDM strategies will change the amplitude distribution of encoded symbol, the peak-to-average power ratio (PAPR) characteristics under different AJSCC parameters are also analyzed. Full article

(This article belongs to the Special Issue Next-Generation Channel Coding: Theory and Applications)

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10 pages, 2135 KiB

Open AccessArticle

High Strength and Fracture Resistance of Reduced-Activity W-Ta-Ti-V-Zr High-Entropy Alloy for Fusion Energy Applications

by Siva Shankar Alla, Blake Kourosh Emad and Sundeep Mukherjee

Entropy 2025, 27(8), 777; https://doi.org/10.3390/e27080777 - 23 Jul 2025

Abstract

Refractory high-entropy alloys (HEAs) are promising candidates for next-generation nuclear applications, particularly fusion reactors, due to their excellent high-temperature mechanical properties and irradiation resistance. Here, the microstructure and mechanical behavior were investigated for an equimolar WTaTiVZr HEA, designed from a palette of low-activation [...] Read more.

Refractory high-entropy alloys (HEAs) are promising candidates for next-generation nuclear applications, particularly fusion reactors, due to their excellent high-temperature mechanical properties and irradiation resistance. Here, the microstructure and mechanical behavior were investigated for an equimolar WTaTiVZr HEA, designed from a palette of low-activation elements. The as-cast alloy exhibited a dendritic microstructure composed of W-Ta rich dendrites and Zr-Ti-V rich inter-dendritic regions, both possessing a body-centered cubic (BCC) crystal structure. Room temperature bulk compression tests showed ultra-high strength of around 1.6 GPa and plastic strain ~6%, with fracture surfaces showing cleavage facets. The alloy also demonstrated excellent high-temperature strength of ~650 MPa at 500 °C. Scratch-based fracture toughness was ~38 MPa√m for the as-cast WTaTiVZr HEA compared to ~25 MPa√m for commercially used pure tungsten. This higher value of fracture toughness indicates superior damage tolerance relative to commercially used pure tungsten. These results highlight the alloy’s potential as a low-activation structural material for high-temperature plasma-facing components (PFCs) in fusion reactors. Full article

(This article belongs to the Special Issue Recent Advances in High Entropy Alloys)

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20 pages, 5416 KiB

Open AccessArticle

A Novel One-Dimensional Chaotic System for Image Encryption Through the Three-Strand Structure of DNA

by Yingjie Su, Han Xia, Ziyu Chen, Han Chen and Linqing Huang

Entropy 2025, 27(8), 776; https://doi.org/10.3390/e27080776 - 23 Jul 2025

Abstract

Digital images have been widely applied in fields such as mobile devices, the Internet of Things, and medical imaging. Although significant progress has been made in image encryption technology, it still faces many challenges, such as attackers using powerful computing resources and advanced [...] Read more.

Digital images have been widely applied in fields such as mobile devices, the Internet of Things, and medical imaging. Although significant progress has been made in image encryption technology, it still faces many challenges, such as attackers using powerful computing resources and advanced algorithms to crack encryption systems. To address these challenges, this paper proposes a novel image encryption algorithm based on one-dimensional sawtooth wave chaotic system (1D-SAW) and the three-strand structure of DNA. Firstly, a new 1D-SAW chaotic system was designed. By introducing nonlinear terms and periodic disturbances, this system is capable of generating chaotic sequences with high randomness and initial value sensitivity. Secondly, a new diffusion rule based on the three-strand structure of DNA is proposed. Compared with the traditional DNA encoding and XOR operation, this rule further enhances the complexity and anti-attack ability of the encryption process. Finally, the security and randomness of the 1D-SAW and image encryption algorithms were verified through various tests. Results show that this method exhibits better performance in resisting statistical attacks and differential attacks. Full article

(This article belongs to the Topic Recent Trends in Nonlinear, Chaotic and Complex Systems)

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19 pages, 782 KiB

Open AccessArticle

On the Rate-Distortion Theory for Task-Specific Semantic Communication

by Jingxuan Chai, Huixiang Zhu, Yong Xiao, Guangming Shi and Ping Zhang

Entropy 2025, 27(8), 775; https://doi.org/10.3390/e27080775 - 23 Jul 2025

Abstract

Semantic communication has attracted considerable interest due to its potential to support emerging human-centric services, such as holographic communications, extended reality (XR), and human-machine interactions. Different from traditional communication systems that focus on minimizing the symbol-level distortion (e.g., bit error rate, signal-to-noise ratio, [...] Read more.

Semantic communication has attracted considerable interest due to its potential to support emerging human-centric services, such as holographic communications, extended reality (XR), and human-machine interactions. Different from traditional communication systems that focus on minimizing the symbol-level distortion (e.g., bit error rate, signal-to-noise ratio, etc.), semantic communication targets at delivering the intended meaning at the destination user which is often quantified by various statistical divergences, often referred to as the semantic distances. Currently, there still lacks a unified framework to quantify the rate-distortion tradeoff for semantic communication with different task-specific semantic distance measures. To tackle this problem, we propose the task-specific rate-distortion theory for semantic communication where different task-specific statistic divergence metrics can be considered. To investigate the impact of different semantic distance measures on the achievable rate, we consider two popular tasks, classification and signal generation. We present the closed-form expressions of the semantic rate-distortion functions for these two different tasks and compare their performance under various scenarios. Extensive experimental results are presented to verify our theoretical results. Full article

(This article belongs to the Special Issue Semantic Information Theory)

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20 pages, 3409 KiB

Open AccessArticle

Order Lot Sizing: Insights from Lattice Gas-Type Model

by Margarita Miguelina Mieras, Tania Daiana Tobares, Fabricio Orlando Sanchez-Varretti and Antonio José Ramirez-Pastor

Entropy 2025, 27(8), 774; https://doi.org/10.3390/e27080774 - 23 Jul 2025

Abstract

In this study, we introduce a novel interdisciplinary framework that applies concepts from statistical physics, specifically lattice-gas models, to the classical order lot-sizing problem in supply chain management. Traditional methods often rely on heuristic or deterministic approaches, which may fail to capture the [...] Read more.

In this study, we introduce a novel interdisciplinary framework that applies concepts from statistical physics, specifically lattice-gas models, to the classical order lot-sizing problem in supply chain management. Traditional methods often rely on heuristic or deterministic approaches, which may fail to capture the inherently probabilistic and dynamic nature of decision-making across multiple periods. Drawing on structural parallels between inventory decisions and adsorption phenomena in physical systems, we constructed a mapping that represented order placements as particles on a lattice, governed by an energy function analogous to thermodynamic potentials. This formulation allowed us to employ analytical tools from statistical mechanics to identify optimal ordering strategies via the minimization of a free energy functional. Our approach not only sheds new light on the structural characteristics of optimal planning but also introduces the concept of configurational entropy as a measure of decision variability and robustness. Numerical simulations and analytical approximations demonstrate the efficacy of the lattice gas model in capturing key features of the problem and suggest promising avenues for extending the framework to more complex settings, including multi-item systems and time-varying demand. This work represents a significant step toward bridging physical sciences with supply chain optimization, offering a robust theoretical foundation for both future research and practical applications. Full article

(This article belongs to the Special Issue Statistical Mechanics of Lattice Gases)

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24 pages, 1832 KiB

Open AccessArticle

Feature Ranking on Small Samples: A Bayes-Based Approach

by Aleksandra Vatian, Natalia Gusarova and Ivan Tomilov

Entropy 2025, 27(8), 773; https://doi.org/10.3390/e27080773 - 22 Jul 2025

Abstract

In the modern world, there is a need to provide a better understanding of the importance or relevance of the available descriptive features for predicting target attributes to solve the feature ranking problem. Among the published works, the vast majority are devoted to [...] Read more.

In the modern world, there is a need to provide a better understanding of the importance or relevance of the available descriptive features for predicting target attributes to solve the feature ranking problem. Among the published works, the vast majority are devoted to the problems of feature selection and extraction, and not the problems of their ranking. In this paper, we propose a novel method based on the Bayesian approach that allows us to not only to build a methodically justified way of ranking features on small datasets, but also to methodically solve the problem of benchmarking the results obtained by various ranking algorithms. The proposed method is also model-free, since no restrictions are imposed on the model. We carry out an experimental comparison of our proposed method with the classical frequency method. For this, we use two synthetic datasets and two public medical datasets. As a result, we show that the proposed ranking method has a high level of self-consistency (stability) already at the level of 50 samples, which is greatly improved compared to classical logistic regression and SHAP ranking. All the experiments performed confirm our theoretical conclusions: with the growth of the sample, an increasing trend of mutual consistency is observed, and our method demonstrates at least comparable results, and often results superior to other methods in the values of self-consistency and monotonicity. The proposed method can be applied to a wide class of rankings of influence factors on small samples, including industrial tasks, forensics, psychology, etc. Full article

(This article belongs to the Section Multidisciplinary Applications)

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32 pages, 1575 KiB

Open AccessArticle

Entropy Accumulation Under Post-Quantum Cryptographic Assumptions

by Ilya Merkulov and Rotem Arnon

Entropy 2025, 27(8), 772; https://doi.org/10.3390/e27080772 - 22 Jul 2025

Abstract

In device-independent (DI) quantum protocols, security statements are agnostic to the internal workings of the quantum devices—they rely solely on classical interactions with the devices and specific assumptions. Traditionally, such protocols are set in a non-local scenario, where two non-communicating devices exhibit Bell [...] Read more.

In device-independent (DI) quantum protocols, security statements are agnostic to the internal workings of the quantum devices—they rely solely on classical interactions with the devices and specific assumptions. Traditionally, such protocols are set in a non-local scenario, where two non-communicating devices exhibit Bell inequality violations. Recently, a new class of DI protocols has emerged that requires only a single device. In this setting, the assumption of no communication is replaced by a computational one: the device cannot solve certain post-quantum cryptographic problems. Protocols developed in this single-device computational setting—such as for randomness certification—have relied on ad hoc techniques, making their guarantees difficult to compare and generalize. In this work, we introduce a modular proof framework inspired by techniques from the non-local DI literature. Our approach combines tools from quantum information theory, including entropic uncertainty relations and the entropy accumulation theorem, to yield both conceptual clarity and quantitative security guarantees. This framework provides a foundation for systematically analyzing DI protocols in the single-device setting under computational assumptions. It enables the design and security proof of future protocols for DI randomness generation, expansion, amplification, and key distribution, grounded in post-quantum cryptographic hardness. Full article

(This article belongs to the Section Quantum Information)

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Entropy, Volume 27, Issue 8 (August 2025) – 15 articles

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