IET Quantum Communication最新文献

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Superposition-Based Abstractions for Quantum Data Encoding Verification 基于叠加的量子数据编码验证抽象
IF 2.5
IET Quantum Communication Pub Date : 2025-04-26 DOI: 10.1049/qtc2.70002
Arun Govindankutty, Sudarshan K. Srinivasan
{"title":"Superposition-Based Abstractions for Quantum Data Encoding Verification","authors":"Arun Govindankutty,&nbsp;Sudarshan K. Srinivasan","doi":"10.1049/qtc2.70002","DOIUrl":"https://doi.org/10.1049/qtc2.70002","url":null,"abstract":"<p>Many quantum algorithms operate on classical data, by first encoding classical data into the quantum domain using quantum data encoding circuits. To be effective for large data sets, encoding circuits that operate on large data sets are required. However, as the size of the data sets increases, the encoding circuits quickly become large, complex and error prone. Errors in the encoding circuit will provide incorrect inputs to quantum algorithms, making them ineffective. To address this problem, a formal method is proposed for verification of encoding circuits. The key idea to address scalability is the use of abstractions that reduce the verification problem to bit-vector space. The major outcome of this work is that using this approach, the authors have been able to verify encoding circuits with up to 8191 qubits with very low memory (85 MB) and time (0.29s), demonstrating that the proposed approach can easily be employed to verify even much larger encoding circuits. The results are very significant because, traditional verification approaches that rely on modelling quantum circuits in Hilbert space have only demonstrated verification scalability up to 250 qubits. Also, this is the first approach to tackle the verification of quantum encoding circuits.</p>","PeriodicalId":100651,"journal":{"name":"IET Quantum Communication","volume":"6 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/qtc2.70002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143877817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Enhance Capacity Region of Multi-Class IIoT Network by Applying Entanglement Assistance Protocol 应用纠缠辅助协议增强多类IIoT网络的容量区域
IF 2.5
IET Quantum Communication Pub Date : 2025-04-24 DOI: 10.1049/qtc2.70001
Doaa Subhi, Laszlo Bacsardi
{"title":"Enhance Capacity Region of Multi-Class IIoT Network by Applying Entanglement Assistance Protocol","authors":"Doaa Subhi,&nbsp;Laszlo Bacsardi","doi":"10.1049/qtc2.70001","DOIUrl":"https://doi.org/10.1049/qtc2.70001","url":null,"abstract":"<p>In the Industrial Internet of Things (IIoT) context, heterogeneous IIoT nodes need diverse performance requirements, including throughput and quality of service (QoS). These IIoT nodes transmit data over a common shared communication medium. The existing critical challenge arises in efficiently scheduling access to this shared medium among a large number of connected IIoT nodes. To address the challenge of random access in IIoT networks, the power of the entanglement-assisted (EA) protocol was exploited to expand the capacity region boundaries of the shared communication medium, thereby enhancing the throughput and quality-of-service (QoS) requirements of the heterogeneous IIoT network. In the literature, IIoT networks are mainly categorised into two types: centralised and distributed. In this paper, we proposed two distinct models: (1) a centralised multi-class IIoT network based on EA protocol and (2) a distributed multi-class IIoT network based on EA protocol. Next, the authors analytically demonstrated that integrating the EA protocol into both proposed types of multi-class IIoT networks significantly increases the capacity region boundaries compared to the classical reference model, namely slotted ALOHA (SA). Finally, the network performance boundaries were evaluated by analysing the throughput values for different network classes and varying numbers of IIoT nodes. The results demonstrate that, for both proposed models (1) and (2), the transmitted load generated by the IIoT nodes over the shared medium achieves dramatically higher throughput compared to the reference IIoT network based on SA.</p>","PeriodicalId":100651,"journal":{"name":"IET Quantum Communication","volume":"6 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/qtc2.70001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Routing in quantum networks with end-to-end knowledge 具有端到端知识的量子网络中的路由
IF 2.5
IET Quantum Communication Pub Date : 2025-02-25 DOI: 10.1049/qtc2.70000
Vinay Kumar, Claudio Cicconetti, Marco Conti, Andrea Passarella
{"title":"Routing in quantum networks with end-to-end knowledge","authors":"Vinay Kumar,&nbsp;Claudio Cicconetti,&nbsp;Marco Conti,&nbsp;Andrea Passarella","doi":"10.1049/qtc2.70000","DOIUrl":"https://doi.org/10.1049/qtc2.70000","url":null,"abstract":"<p>Given the diverse array of physical systems available for quantum computing and the absence of a well-defined quantum Internet protocol stack, the design and optimisation of quantum networking protocols remain largely unexplored. To address this, the authors introduce an approach that facilitates the establishment of paths capable of delivering end-to-end fidelity above a specified threshold, without requiring detailed knowledge of the quantum network's properties. In this study, the authors define algorithms that are specific instances of this approach and evaluate them in comparison to Dijkstra's shortest path algorithm and a fully knowledge-aware algorithm through simulations. The authors’ results demonstrate that one of the proposed algorithms consistently outperforms the other methods in delivering paths above the fidelity threshold, across various network topologies and the number of source-destination pairs involved, while maintaining significant levels of fairness among the users and being robust to inaccurate estimations of the expected end-to-end fidelity.</p>","PeriodicalId":100651,"journal":{"name":"IET Quantum Communication","volume":"6 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/qtc2.70000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143481376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Beamforming optimization via quantum algorithms using Variational Quantum Eigensolver and Quantum Approximate Optimization Algorithm 基于变分量子特征解算器和量子近似优化算法的量子波束形成优化
IF 2.5
IET Quantum Communication Pub Date : 2025-02-12 DOI: 10.1049/qtc2.12120
Bidisha Dhara, Monika Agrawal, Sumantra Dutta Roy
{"title":"Beamforming optimization via quantum algorithms using Variational Quantum Eigensolver and Quantum Approximate Optimization Algorithm","authors":"Bidisha Dhara,&nbsp;Monika Agrawal,&nbsp;Sumantra Dutta Roy","doi":"10.1049/qtc2.12120","DOIUrl":"https://doi.org/10.1049/qtc2.12120","url":null,"abstract":"<p>This study investigates the application of quantum algorithms, specifically the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA), to design optimal sensor configurations for beamforming, enhancing signal quality and overall system performance. We propose two distinct optimization formulations: one aimed at maximising array gain while the other aimed at maximising signal-to-noise-interference ratio (SINR). Our findings show that the outputs obtained from quantum algorithms are consistent with those derived from classical methods.</p>","PeriodicalId":100651,"journal":{"name":"IET Quantum Communication","volume":"6 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/qtc2.12120","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum teleportation in higher dimension and entanglement distribution via quantum switches 高维量子隐形传态及量子开关的纠缠分布
IF 2.5
IET Quantum Communication Pub Date : 2025-01-24 DOI: 10.1049/qtc2.12122
Indrakshi Dey, Nicola Marchetti
{"title":"Quantum teleportation in higher dimension and entanglement distribution via quantum switches","authors":"Indrakshi Dey,&nbsp;Nicola Marchetti","doi":"10.1049/qtc2.12122","DOIUrl":"https://doi.org/10.1049/qtc2.12122","url":null,"abstract":"<p>High-dimensional quantum states, or ‘qudits’, provide significant advantages over traditional qubits in quantum communication, such as increased information capacity, enhanced noise resilience, and reduced information loss. Despite these benefits, their implementation has been constrained by challenges in generation, transmission, and detection. This paper presents a novel theoretical framework for transmitting quantum information using qudit entanglement distribution over a superposition of causal orders in two quantum channels. Using this model, a quantum switch operation for 2-qudit systems is introduced, which facilitates enhanced fidelity of entanglement distribution and quantum teleportation. The results demonstrate that the use of qudits in entanglement distribution achieves a fidelity improvement from 0.5 (for qubit-based systems) to 0.94 for 20-dimensional qudits, even under noisy channel conditions. This enhancement is achieved by exploiting the increased Hilbert space of high-dimensional states and the inherent noise-resilience properties of quantum switches operating in superpositions of causal orders. The findings underscore the potential of qudit-based quantum systems in achieving robust and high-fidelity communication in environments where traditional qubit-based systems face limitations.</p>","PeriodicalId":100651,"journal":{"name":"IET Quantum Communication","volume":"6 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/qtc2.12122","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Entanglement swapping using hyperentangled pairs of two-level neutral atoms 利用超纠缠对的两能级中性原子进行纠缠交换
IF 2.5
IET Quantum Communication Pub Date : 2025-01-11 DOI: 10.1049/qtc2.12121
Syed Sajal Hasan, Syed Muhammad Arslan Anis, Muhammad Imran, Rameez-ul Islam, Saif Al-Kuwari, Tasawar Abbas
{"title":"Entanglement swapping using hyperentangled pairs of two-level neutral atoms","authors":"Syed Sajal Hasan,&nbsp;Syed Muhammad Arslan Anis,&nbsp;Muhammad Imran,&nbsp;Rameez-ul Islam,&nbsp;Saif Al-Kuwari,&nbsp;Tasawar Abbas","doi":"10.1049/qtc2.12121","DOIUrl":"https://doi.org/10.1049/qtc2.12121","url":null,"abstract":"<p>Hyperentangled swapping is a quantum communication technique that involves the exchange of hyperentangled states, which are quantum states entangled in multiple degrees of freedom, to enable secure and efficient quantum information transfer. In this paper, we demonstrate schematics for the hyperentanglement swapping between separate pairs of neutral atoms through the mathematical framework of atomic Bragg diffraction, which is efficient and resistant to decoherence, yielding deterministic results with superior overall fidelity. The utilised cavities are in a superposition state and interact with the incoming atoms off-resonantly. Quantum information carried by the cavities is swapped through resonant interactions with two-level auxiliary atoms. We also discuss entanglement swapping under a delayed-choice scenario and provide a schematic generalisation covering multiple-qubit scenarios. Finally, we introduce specific experimental parameters to demonstrate the experimental feasibility of the scheme.</p>","PeriodicalId":100651,"journal":{"name":"IET Quantum Communication","volume":"6 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/qtc2.12121","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Review on 6G communication and its architecture, technologies included, challenges, security challenges and requirements, applications, with respect to AI domain 回顾了人工智能领域的6G通信及其架构、技术、挑战、安全挑战和需求、应用
IF 2.5
IET Quantum Communication Pub Date : 2024-12-30 DOI: 10.1049/qtc2.12114
Pranita Bhide, Dhanush Shetty, Suresh Mikkili
{"title":"Review on 6G communication and its architecture, technologies included, challenges, security challenges and requirements, applications, with respect to AI domain","authors":"Pranita Bhide,&nbsp;Dhanush Shetty,&nbsp;Suresh Mikkili","doi":"10.1049/qtc2.12114","DOIUrl":"https://doi.org/10.1049/qtc2.12114","url":null,"abstract":"<p>The evolution of wireless communication systems has led to the emergence of the sixth generation (6G) communication architecture, characterised by transformative technologies and novel paradigms that transcend the capabilities of its predecessors. This paper presents an overview of the various aspects of 6G communication architecture, focusing on its technologies, challenges, and applications within the domain of artificial intelligence (AI). The abstract provides an overview of a review on 6G communication, focusing on its architecture, technologies, challenges, security concerns, and requirements within the context of the AI domain. The paper explores the evolving landscape of wireless communication, delving into the anticipated features and capabilities of 6G networks. The architecture emphasises the integration of AI-driven elements, such as intelligent resource allocation and autonomous network management. Various technologies, including terahertz frequencies and integrated satellite networks, are discussed in terms of their potential to reshape connectivity paradigms. However, alongside the promises, a multitude of challenges arise. These encompass spectrum scarcity at terahertz frequencies, energy efficiency concerns, and the need for global standardisation. Addressing security challenges is crucial, considering the expanded attack surface and the integration of AI-powered functionalities. The paper also delineates the stringent requirements that 6G must fulfil, spanning ultra-low latency, high bandwidth, massive device connectivity, and reliable communication. Contextualising these discussions, the review highlights applications within the AI domain that stand to benefit from 6G advancements. These include edge AI, augmented reality, autonomous systems, and IoT-enabled environments. By synergising cutting-edge wireless capabilities with AI-driven intelligence, 6G is poised to revolutionise industries and societal experiences in unprecedented ways.</p>","PeriodicalId":100651,"journal":{"name":"IET Quantum Communication","volume":"6 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/qtc2.12114","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum blockchain: Trends, technologies, and future directions 量子区块链:趋势、技术和未来方向
IF 2.5
IET Quantum Communication Pub Date : 2024-12-11 DOI: 10.1049/qtc2.12119
Manjula Gandhi S, Chaitrali Mulay, Karthiganesh Durai, G. Murali, Jafar Ali Ibrahim Syed Masood, V. Vijayarajan, Kumar Gautam, N. S. Kalyan Chakravarthy, S. Suresh Kumar, Saurabh Agarwal, Murali S, Vijayasherly V, David Asirvatham, Sarfraz Brohi, Chandru Vignesh C, Anbuchelian S
{"title":"Quantum blockchain: Trends, technologies, and future directions","authors":"Manjula Gandhi S,&nbsp;Chaitrali Mulay,&nbsp;Karthiganesh Durai,&nbsp;G. Murali,&nbsp;Jafar Ali Ibrahim Syed Masood,&nbsp;V. Vijayarajan,&nbsp;Kumar Gautam,&nbsp;N. S. Kalyan Chakravarthy,&nbsp;S. Suresh Kumar,&nbsp;Saurabh Agarwal,&nbsp;Murali S,&nbsp;Vijayasherly V,&nbsp;David Asirvatham,&nbsp;Sarfraz Brohi,&nbsp;Chandru Vignesh C,&nbsp;Anbuchelian S","doi":"10.1049/qtc2.12119","DOIUrl":"https://doi.org/10.1049/qtc2.12119","url":null,"abstract":"<p>Blockchain technology is a highly developed database system that shares information within a business web. It stores details in blocks connected chronologically, ensuring information integrity through consensus mechanisms that prevent unauthorised alterations. This decentralised system removes the need for a believable mediator, mitigating vulnerabilities and enhancing transaction security. Blockchain’s application spans the energy, finance, media, entertainment, and retail sectors. However, classical blockchain faces threats from quantum computing advancements, necessitating the development of quantum blockchain technology. Quantum blockchain, leveraging quantum computation and information theory, offers enhanced security and immutability. In this paper, different mathematical foundations, practical implementations and effectiveness of lattice-based cryptography in securing blockchain applications are discussed. Analysis of how the cryptographic techniques can protect blockchain systems against quantum attacks is being done by using mathematical formulations and examples. Quantum computing strengthens blockchain security with advanced encryption and authentication, which is critical for safeguarding diverse sectors from evolving cyber threats. Further study on quantum-resistant design is necessary if blockchain networks are to be robust and intact in the face of future technological developments.</p>","PeriodicalId":100651,"journal":{"name":"IET Quantum Communication","volume":"5 4","pages":"516-542"},"PeriodicalIF":2.5,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/qtc2.12119","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143252533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Real-time seedless post-processing for quantum random number generators 量子随机数生成器的实时无籽后处理
IF 2.5
IET Quantum Communication Pub Date : 2024-12-11 DOI: 10.1049/qtc2.12118
Qian Li, Hongyi Zhou
{"title":"Real-time seedless post-processing for quantum random number generators","authors":"Qian Li,&nbsp;Hongyi Zhou","doi":"10.1049/qtc2.12118","DOIUrl":"https://doi.org/10.1049/qtc2.12118","url":null,"abstract":"<p>Quantum-proof randomness extraction is essential for handling quantum side information possessed by a quantum adversary, which is widely applied in various quantum cryptography tasks. In this study, the authors introduce a real-time two-source quantum randomness extractor against quantum side information. The authors’ extractor is tailored for forward block sources, a novel category of min-entropy sources introduced in this work. These sources retain the flexibility to accommodate a broad range of quantum random number generators. The authors’ online algorithms demonstrate the extraction of a constant fraction of min-entropy from two infinitely long independent forward block sources. Moreover, the authors’ extractor is inherently block-wise parallelisable, presenting a practical and efficient solution for the timely extraction of high-quality randomness. Applying the authors’ extractors to the raw data of one of the most commonly used quantum random number generators, a simulated extraction speed as high as 64 Gbps is achieved.</p>","PeriodicalId":100651,"journal":{"name":"IET Quantum Communication","volume":"5 4","pages":"650-657"},"PeriodicalIF":2.5,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/qtc2.12118","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143252349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum anonymous one vote veto protocol based on entanglement swapping 基于纠缠交换的量子匿名一票否决协议
IF 2.5
IET Quantum Communication Pub Date : 2024-12-03 DOI: 10.1049/qtc2.12117
Yanmeng Wang, Min Jiang, Yuzhen Wei, Wenhao Zhao
{"title":"Quantum anonymous one vote veto protocol based on entanglement swapping","authors":"Yanmeng Wang,&nbsp;Min Jiang,&nbsp;Yuzhen Wei,&nbsp;Wenhao Zhao","doi":"10.1049/qtc2.12117","DOIUrl":"https://doi.org/10.1049/qtc2.12117","url":null,"abstract":"<p>As a special voting method, one-vote veto voting also has a wide range of applications. A veto means that when the voting council puts forward a proposal, it cannot pass unless all the voters agree to it. If there is a no vote, the proposal will be rejected, but no one will know how anyone else votes. In most existing quantum anonymous one-vote veto voting protocols, an absolutely honest third party is generally required to assist the voting. However, it is difficult to find a fully trusted third party in reality. In addition, the existing quantum anonymous one-vote veto protocol does not consider the attack from the insider voters. Therefore, based on the characteristics of entanglement swapping between the Cat state and Bell state, the authors propose a new quantum anonymous one-vote veto protocol, which can not only calculate the voting result quickly and effectively but also demonstrate higher security.</p>","PeriodicalId":100651,"journal":{"name":"IET Quantum Communication","volume":"5 4","pages":"641-649"},"PeriodicalIF":2.5,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/qtc2.12117","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143248326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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