اصول نظریه کوانتومی اطلاعات و قابلیت‌های آن در بازیابی اطلاعات

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه علم اطلاعات و دانش‌‏شناسی، دانشکده علوم تربیتی و روان‏شناسی، دانشگاه شهید بهشتی، تهران، ایران.

2 گروه علم اطلاعات و دانش‏‌شناسی، دانشکده علوم تربیتی و روان‏شناسی، دانشگاه شهید بهشتی، تهران، ایران.

چکیده
این پژوهش با هدف اصلی تحلیل قابلیت‏‌های نظریه کوانتومی اطلاعات در بهبود فرایندهای بازیابی اطلاعات انجام شده است. پژوهش به دنبال پاسخ به این مسئله است که چگونه می‏‌توان از اصول بنیادی مکانیک کوانتومی برای رفع چالش‏‌های موجود در سیستم‌‏های بازیابی اطلاعات سنتی بهره برد. پژوهش حاضر با استفاده از روش کتابخانه‏‌ای و رویکرد تحلیلی-مروری انجام شده است. در این راستا، با مرور جامع ادبیات نظری، مفاهیم بنیادین نظریه کوانتومی اطلاعات شناسایی و سپس ارتباط مفهومی و کاربردی آن‏ها با حوزه بازیابی اطلاعات به‌‏صورت نظام‏مند تحلیل گردیده است. یافته‏‌ها نشان می‏دهد که نظریه کوانتومی اطلاعات از طریق مفاهیمی چون برهم‏نهی و درهم‏تنیدگی، چارچوب جدیدی برای نمایش، پردازش و بازیابی اطلاعات فراهم می‌‏کند. به‏‌کارگیری پدیده‏‌هایی مانند الگوریتم‌‏های کوانتومی و تصحیح خطای کوانتومی می‏‌تواند به‌‏طور چشم‌گیری دقت و سرعت بازیابی اطلاعات را افزایش دهد. این رویکرد با یکپارچه‌‏سازی جنبه‌‏های بازنمایی، رتبه‌‏بندی و شناختی کاربر، راهکارهایی برای توسعه سیستم‏‌های پویاتر و آگاه به زمینه ارائه می‌‏دهد. علی‏رغم وجود موانع فنی و نظری، نظریه کوانتومی اطلاعات پتانسیل ایجاد یک تحول بنیادین در حوزه بازیابی اطلاعات را داراست. انتظار می‌‏رود با پیشرفت تحقیقات در این زمینه، فناوری‏‌های نوینی مبتنی بر اصول کوانتومی توسعه یابند که منجر به افزایش کارایی، امنیت و دقت در سیستم‏های بازیابی اطلاعات آینده خواهد شد.

کلیدواژه‌ها

موضوعات

عنوان مقاله English

Principles of Quantum Information Theory and Its Capabilities in Information Retrieval

نویسندگان English

Pourya Rahat 1
Mohsen Haji Zeinolabedini 2
1 Department of Information Science, Faculty of Psychology and Educational Sciences, Shahid Beheshti University, Tehran, Iran.
2 Department of Information Science, Faculty of Psychology and Educational Sciences, Shahid Beheshti University, Tehran, Iran.
چکیده English

Introduction
Quantum information is a general form of information that can be considered the fundamental material of the universe (Penchev, 2020). Its basic unit is the qubit, which, unlike a classical bit's binary 0 or 1 state, can exist in multiple states simultaneously. This phenomenon, known as superposition, allows a qubit to be a linear combination of states (Nielsen & Chuang, 2010), enabling quantum parallelism and an exponential increase in computational power. Quantum Information Theory (QIT) explores these principles, along with other key concepts such as entanglement, where qubits become interdependent regardless of distance; the no-cloning theorem, which makes it impossible to create an identical copy of an unknown quantum state; and practical applications like quantum error correction and quantum cryptography. While traditional Information Retrieval (IR) is built on core concepts like Boolean, vector space, and probabilistic models (Melucci, 2015; Tunkelang & Thelwall, 2009; Büttcher et al., 2010; Gudivada et al., 2018), QIT provides a new framework to enhance it. This theory offers a way to unify the representation, ranking, and cognitive aspects of the user by applying the formalism and mathematics of quantum mechanics. This connection is often inspired by the theory and applied to classical computers, drawing on the broad use of quantum principles in cognitive science, psychology, and decision-making (Ashoori & Rudolph, 2018; Lebedev & Khrennikov, 2020). This paper aimed to review the fundamental principles of QIT, analyze their relevance to IR, and present the opportunities and challenges at the intersection of these two fields.
Literature Review
The intersection of QIT and IR has evolved from foundational theoretical work to practical and evaluative models. Early research by Piwowarski et al. (2010) proposed a quantum framework to address key IR challenges like interaction, novelty, and diversity, a view expanded by van Rijsbergen (2011), who argued that quantum formalism is the appropriate language for modeling the uncertainty inherent in information. Subsequent studies demonstrated the application of quantum mathematics, such as the "Quantum Probability Ranking Principle" for ranking interdependent documents (Zuccon & Azzopardi, 2010) and the use of quantum theory for "quantum-like" modeling (Khrennikov, 2019) and meaning-focused retrieval (Aerts et al., 2013). More recently, the field has moved toward integrating quantum principles with deep learning, as seen in quantum-inspired neural matching models (Jiang et al., 2020), and addressing security through protocols like quantum private information retrieval (Yang et al., 2023). This progression indicates a shift from purely theoretical explorations (Ashoori & Rudolph, 2018) to the development of practical evaluation frameworks (Ferrari Dacrema et al., 2024) and new contextual search methods (Alodjants et al., 2024).
Methodology
This study was conducted as fundamental research, employing an analytical-review method appropriate for the theoretical and emerging nature of the topic. Data collection started with documentary research, using defined keywords to systematically gather sources from databases such as Web of Science and Google Scholar. Following the screening and selection of relevant literature, the research utilized an approach of conceptual analysis and literature synthesis. Foundational concepts from Quantum Information Theory were first extracted and broken down. Then, in the synthesis phase, these concepts were systematically linked to the challenges, needs, and processes of Information Retrieval to build a logical and applied bridge between the two fields.
Results
The results of this analysis are presented in two main parts. First, the foundational concepts of Quantum Information Theory (QIT) are detailed, organized into three categories: fundamental concepts, including qubits, quantum states, superposition, entanglement, and quantum entropy; principles and theories, such as quantum algorithms and the no-cloning theorem; and applications, like quantum error correction, cryptography, and quantum gates. The second part of the results systematically connects these principles to the domain of Information Retrieval (IR). The results demonstrated how concepts like superposition can offer a probabilistic framework for relevance, how quantum algorithms, such as Grover's algorithm, can exponentially speed up search, and how quantum entanglement and error correction can be used to model complex term dependencies and ensure the security and integrity of the retrieval process, respectively.
Discussion
The theoretical alignment between Quantum Information Theory (QIT) and Information Retrieval (IR) suggests that quantum principles are exceptionally well-suited to address the core limitations of classical IR systems, particularly the complex issues of context, ambiguity, and human cognition. The inherent probabilistic nature of quantum states, governed by superposition, offers a formal mathematical framework for modeling the fuzzy and subjective concept of relevance more dynamically than traditional vector-space models. Furthermore, the concept of entanglement provides a powerful mechanism to model the nonlocal dependencies between index terms, documents, and user intent, moving beyond simple co-occurrence counts to capture holistic conceptual relationships. The analysis highlighted that while the full power of quantum computing is not always necessary for these benefits, as evidenced by successful quantum-like (QL) models running on classical hardware, the ultimate, exponential performance gains promised by algorithms like Grover's algorithm for database searching remain the strongest long-term motivation for future IR systems to leverage true quantum hardware.
Conclusion
By analytically comparing the core principles of Quantum Information Theory (QIT) and identifying their points of convergence with classical information retrieval systems, this research confirmed that Quantum Information Theory offered a potent, mathematically grounded framework with the potential to fundamentally transform the field of Information Retrieval. By leveraging quantum principles (such as superposition to model the inherent uncertainty of relevance and entanglement to capture complex, nonlocal dependencies between terms) future IR systems could overcome the cognitive and structural limitations of classical models. While the full deployment of quantum algorithms like Grover's algorithm on dedicated quantum hardware promised exponential speed and efficiency gains in the long term, even the adoption of QL models on existing classical infrastructure could yield significant, immediate improvements in accuracy, security, and contextual awareness. Despite existing technical and theoretical obstacles, it was anticipated that continued research in this area would lead to innovative technologies based on quantum principles, resulting in enhanced precision and efficiency in future information retrieval systems.

کلیدواژه‌ها English

Information Retrieval
Quantum Computing
Quantum Information Theory
Quantum Systems
Quantum Mechanics
تقی‏زاده کورایم، فرناز، کاباران‏زاد قدیم، محمدرضا، و موسوی، سیدعبداله امین. (۱۴۰۵). استفاده از انتخابگرهای پویا و هوش مصنوعی برای مقاوم‏سازی کدهای بازیابی اطلاعات وب. فصلنامه بازیابی دانش و نظام‏های معنایی، ۱۳(۴۶)، ۱–۲۴. https://doi.org/10.22054/jks.2026.89870.1753
هلاکویان، سیده نجمه، بهزادی، حسن، و ارسطوپور، شعله. (۱۴۰۵). تأثیر تحریف‏های شناختی بر بازیابی اطلاعات: یک تحلیل رفتاری در مراحل مختلف جستجو. فصلنامه بازیابی دانش و نظام‏های معنایی، ۱۲(۴۵)، ۱–۳۴. https://doi.org/10.22054/jks.2025.86648.1727
References
Aerts, D., Broekaert, J., Sozzo, S., & Veloz, T. (2013). Meaning-focused and quantum-inspired information retrieval. In Quantum interaction (pp. 69–80). Springer. https://doi.org/10.1007/978-3-642-54943-4_7
Alodjants, A. P., Avdyushina, A. E., Tsarev, D. V., Bessmertny, I. A., & Khrennikov, A. Y. (2024). Quantum approach for contextual search, retrieval, and ranking of classical information. Entropy, 26(10), Article 862. https://doi.org/10.3390/e26100862
Anza, F., & Crutchfield, J. P. (2022). Quantum information dimension and geometric entropy. PRX Quantum, 3(2), Article 020355. https://doi.org/10.1103/PRXQuantum.3.020355
Aoki, T., Takahashi, G., Kajiya, T., Yoshikawa, J.-I., Braunstein, S. L., van Loock, P., & Furusawa, A. (2009). Quantum error correction beyond qubits. Nature Physics, 5(8), 541–546. https://doi.org/10.1038/nphys1309
Archuadze, M., Besiashvili, G., Khachidze, M., & Kervalishvili, P. (2012). Quantum concepts in information retrieval. In 2012 6th International Conference on Application of Information and Communication Technologies (AICT) (pp. 1–4). IEEE. https://doi.org/10.1109/ICAICT.2012.6398524
Ashoori, E., & Rudolph, T. (2018). Commentary on quantum-inspired information retrieval. arXiv. https://doi.org/10.48550/arXiv.1809.05685
Averin, D. (1999). Quantum computation: Solid-state qubits under control. Nature, 398(6730), 748–749. https://doi.org/10.1038/19622
Baaquie, B. E., & Kwek, L.-C. (2023). Quantum gates and circuits. In Quantum computers (pp. 139–153). Springer. https://doi.org/10.1007/978-981-19-7517-2_7
Bandyopadhyay, S. (2020). Impossibility of creating a superposition of unknown quantum states. Physical Review A, 102(5), Article 050202. https://doi.org/10.1103/PhysRevA.102.050202
Bassi, R., Zhang, Q., Gatto, A., Tornatore, M., & Verticale, G. (2023). Quantum key distribution with trusted relay using an ETSI-compliant software-defined controller. In 2023 19th International Conference on the Design of Reliable Communication Networks (DRCN) (pp. 1–7). IEEE. https://doi.org/10.1109/DRCN57075.2023.10108347
Baudot, P., & Bennequin, D. (2015). The homological nature of entropy. Entropy, 17(5), 3253–3318. https://doi.org/10.3390/e17053253
Benhelm, J., Kirchmair, G., Gerritsma, R., Zähringer, F., Monz, T., Schindler, P., ... & Blatt, R. (2009). 40Ca+ quantum bits for quantum information processing. Physica Scripta, 2009(T137), Article 014008. https://doi.org/10.1088/0031-8949/2009/T137/014008
Bergou, J. A., & Hillery, M. S. (2013). Introduction to the theory of quantum information processing. Springer. https://doi.org/10.1007/978-1-4614-7092-2
Bernstein, B. (2023). Quantum cryptography. In Quantum computing: Physics, blockchains, and cryptography (pp. 241–264). Wiley. https://doi.org/10.1002/9781119905172.ch14
Brańczyk, A., Mendonca, P., Gilchrist, A., Doherty, A., & Bartlett, S. (2006). Quantum control of a single qubit. Physical Review A, 75(1), Article 012329. https://doi.org/10.1103/PhysRevA.75.012329
Buot, F. A., Otadoy, R. E. S., & Bacalla, X. L. (2023). An inverter-chain link implementation of quantum teleportation and superdense coding. arXiv. https://doi.org/10.48550/arXiv.2312.03276
Büttcher, S., Clarke, C. L., & Cormack, G. V. (2010). Information retrieval: Implementing and evaluating search engines. MIT Press.
Caleffi, M., & Cacciapuoti, A. S. (2019). Quantum switch for the quantum internet: Noiseless communications through noisy channels. IEEE Journal on Selected Areas in Communications, 38(3), 575–588. https://doi.org/10.1109/JSAC.2020.2969035
Cole, B., Williams, J., King, B., Sherwin, M., & Stanley, C. (2001). Coherent manipulation of semiconductor quantum bits with terahertz radiation. Nature, 410(6824), 60–63. https://doi.org/10.1038/35065032
Conway, J., & Kochen, S. (2006). The free will theorem. Foundations of Physics, 36(10), 1441–1473. https://doi.org/10.1007/s10701-006-9068-6
Conway, J., & Kochen, S. (2009). The strong free will theorem. Notices of the AMS, 56(2), 226–232.
Cozzolino, D., Bacco, D., Lio, B., Ingerslev, K., Ding, Y., Dalgaard, K., ... & Oxenløwe, L. (2018). Orbital angular momentum states enabling fiber-based high-dimensional quantum communication. Physical Review Applied, 11(6), Article 064058. https://doi.org/10.1103/PhysRevApplied.11.064058
Das, D., Malapaka, S. K., Bapat, J., & Das, D. (2022). A proactive connection setup mechanism for large quantum networks. In 2022 IEEE International Conference on Electronics, Computing and Communication Technologies (CONECCT) (pp. 1–6). IEEE. https://doi.org/10.1109/CONECCT55679.2022.9865700
De Julio, M. (2022). On quantum entropy. Entropy, 24(10), Article 1341. https://doi.org/10.3390/e24101341
Devitt, S. J., Nemoto, K., & Munro, W. J. (2009). Quantum error correction for beginners. arXiv. https://doi.org/10.48550/arXiv.0905.2794
Dmytrovych, B. V., & Volodymyrovich, B. V. (2017). Quantum-mechanical aspects of the L. Pauling's resonance theory. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.3065282
Duff, G. F. D. (1964). On the principle of superposition in quantum mechanics. Canadian Mathematical Bulletin, 7(1), 77–83. https://doi.org/10.4153/CMB-1964-010-5
Dvali, G. (2021). Bounds on quantum information storage and retrieval. arXiv. https://doi.org/10.48550/arXiv.2105.00995
Ellerman, D. (2018). Logical entropy: Introduction to classical and quantum logical information theory. Entropy, 20(9), Article 679. https://doi.org/10.3390/e20090679
Emeriau, P.-E., Howard, M., & Mansfield, S. (2020). Quantum advantage in information retrieval. arXiv. https://doi.org/10.48550/arXiv.2009.05581
Ferrari Dacrema, M., Pasin, A., Cremonesi, P., & Ferro, N. (2024). Using and evaluating quantum computing for information retrieval and recommender systems. In Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval (pp. 3017–3020). ACM. https://doi.org/10.1145/3626772.3661378
Flarend, A., & Hilborn, B. (2022). Qubits and quantum states. In Quantum computing: From Alice to Bob (pp. 25–43). Oxford University Press. https://doi.org/10.1093/oso/9780192857972.003.0004
Frigyik, A. (2022). Quantum cryptography: Quantum key distribution, a non-technical approach. arXiv. https://doi.org/10.48550/arXiv.2211.17089
Gerry, C. C., & Bruno, K. M. (2013). Quantum information, quantum cryptography, and quantum teleportation. In The quantum divide (pp. 132–148). Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199666560.003.0006
Giri, P. R., & Korepin, V. E. (2017). A review on quantum search algorithms. Quantum Information Processing, 16(12), Article 315. https://doi.org/10.1007/s11128-017-1768-7
Girling, M., Cîrstoiu, C., & Jennings, D. (2023). A simple formulation of no-cloning and no-hiding that admits efficient and robust verification. arXiv. https://doi.org/10.48550/arXiv.2307.03197
Giroti, I., & Malhotra, M. (2022). Quantum cryptography: A pathway to secure communication. In 2022 IEEE International Conference on Current Trends in Advanced Computing (ICCTAC) (pp. 1–6). IEEE. https://doi.org/10.1109/CSITSS57437.2022.10026388
Gudder, S. P. (1970). A superposition principle in physics. Journal of Mathematical Physics, 11(3), 1037–1040. https://doi.org/10.1063/1.1665193
Gudivada, V. N., Rao, D., & Gudivada, A. R. (2018). Information retrieval: Concepts, models, and systems. In Handbook of statistics (Vol. 38, pp. 331–401). Elsevier. https://doi.org/10.1016/bs.host.2018.07.009
Guowen, W. (2005). Locality of quantum entanglement. arXiv. https://doi.org/10.48550/arXiv.quant-ph/0512195
Gushanskiy, S., Potapov, V., & Bozhich, V. I. (2022). Research and development of a quantum code for error correction. Izvestiya SFedU. Engineering Sciences, (3), 129–139. https://doi.org/10.18522/2311-3103-2022-3-129-139
Halakoyan, S. N., Behzadi, H., & Arastoopoor, S. (2026). The influence of cognitive distortions on information retrieval: A behavioral analysis across search stages. Knowledge Retrieval and Semantic Systems, 12(45), 1–34. https://doi.org/10.22054/jks.2025.86648.1727 [In Persian]
Hall, M. J. (1994). Gaussian noise and quantum-optical communication. Physical Review A, 50(4), 3295–3303. https://doi.org/10.1103/PhysRevA.50.3295
Hamidi-rad, S., & Kaewell, J. D. (2022). Quantum channel decoding. In 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) (pp. 675–676). IEEE. https://doi.org/10.1109/QCE53715.2022.00141
Henderson, L. J., Belenchia, A., Castro-Ruiz, E., Budroni, C., Zych, M., Brukner, Č., & Mann, R. B. (2020). Quantum temporal superposition: The case of quantum field theory. Physical Review Letters, 125(13), Article 131602. https://doi.org/10.1103/PhysRevLett.125.131602
Hirche, C. (2015). Polar codes in quantum information theory. arXiv. https://doi.org/10.48550/arXiv.1501.03737
Hirche, C., Morgan, C., & Wilde, M. M. (2016). Polar codes in network quantum information theory. IEEE Transactions on Information Theory, 62(2), 915–924. https://doi.org/10.1109/TIT.2016.2514319
Holbrook, J. A., Kribs, D. W., Laflamme, R., & Poulin, D. (2005). Noiseless subsystems for collective rotation channels in quantum information theory. Integral Equations and Operator Theory, 51(2), 215–234. https://doi.org/10.1007/s00020-004-1345-1
Holevo, A. S. (1997). Coding theorems for quantum communication channels. arXiv. https://doi.org/10.48550/arXiv.quant-ph/9708046
Horodecki, M., & Horodecki, R. (1997). Are there basic laws of quantum information processing? arXiv. https://doi.org/10.48550/arXiv.quant-ph/9705003
Jiang, Y., Zhang, P., Gao, H., & Song, D. (2020). A quantum interference inspired neural matching model for ad-hoc retrieval. In Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval (pp. 19–28). ACM. https://doi.org/10.1145/3397271.3401089
Kavuri, R., Voruganti, S., Mohammed, S., Inapanuri, S., & Harish Goud, B. (2023). Quantum cryptography with an emphasis on the security analysis of QKD protocols. In Evolution and applications of quantum computing (pp. 265–288). Wiley. https://doi.org/10.1002/9781119905172.ch16
Khalifa, O. O., Amirah bt Sharif, N., Saeed, R. A., Abdel-Khalek, S., Alharbi, A. N., & Alkathiri, A. A. (2021). Digital system design for quantum error correction codes. Contrast Media & Molecular Imaging, 2021, Article 1101911. https://doi.org/10.1155/2021/1101911
Khan, K. (2023). Error correction using quantum computation. Journal of Digital Science, 5(1), 16–28. https://doi.org/10.33847/2686-8296.5.1_2
Khrennikov, A. (2019). Basics of quantum theory for quantum-like modeling information retrieval. In Quantum-like models for information retrieval and decision-making (pp. 67–85). Springer. https://doi.org/10.1007/978-3-030-25913-6_4
Kohnle, A., & Deffebach, E. (2015). Investigating student understanding of quantum entanglement. arXiv. https://doi.org/10.48550/arXiv.1512.02346
Kok, P., & Lovett, B. W. (2010). Quantum information processing. In Introduction to optical quantum information processing (pp. 48–89). Cambridge University Press. https://doi.org/10.1017/CBO9781139193658.003
Korsbakken, J. I., Wilhelm, F. K., & Whaley, K. B. (2009). Electronic structure of superposition states in flux qubits. Physica Scripta, 2009(T137), Article 014022. https://doi.org/10.1088/0031-8949/2009/T137/014022
Kovachy, T., Asenbaum, P., Overstreet, C., Donnelly, C. A., Dickerson, S. M., Sugarbaker, A., ... & Kasevich, M. A. (2015). Quantum superposition at the half-metre scale. Nature, 528(7583), 530–533. https://doi.org/10.1038/nature16155
Kretschmann, D., Kribs, D. W., & Spekkens, R. W. (2008). Complementarity of private and correctable subsystems in quantum cryptography and error correction. Physical Review A, 78(3), Article 032330. https://doi.org/10.1103/PhysRevA.78.032330
Kurizki, G., & Gordon, G. (2020). What is a quantum superposition? In The quantum matrix (pp. 21–38). Oxford University Press. https://doi.org/10.1093/oso/9780198787464.003.0002
Kwon, H., & Bae, J. (2022). Quantum amplitude amplification operators: Exact quantum search. In K. S. Deacon & R. E. Meyers (Eds.), Quantum communications and quantum imaging XX (Vol. 12224, pp. 10–17). SPIE. https://doi.org/10.1117/12.2626449
Lebedev, A., & Khrennikov, A. (2020). Introductory review to quantum information retrieval. arXiv. https://doi.org/10.48550/arXiv.2008.13541
Lent, C. S. (2019). Information and entropy in physical systems. In Energy limits in computation (pp. 1–63). Springer. https://doi.org/10.1007/978-3-319-93458-7_1
Li, J. (2020). Some progress on quantum error correction for discrete and continuous error models. IEEE Access, 8, 46998–47012. https://doi.org/10.1109/ACCESS.2020.2977344
Lima, F. C. E., Moreira, A. R. P., Almeida, C. A. S., Edet, C. O., & Ali, N. (2023). Quantum information entropy of a particle trapped by the Aharonov–Bohm-type effect. Physica Scripta, 98(6), Article 065111. https://doi.org/10.1088/1402-4896/acd309
Liu, Z., Xie, Q., Zha, Y., & Dong, Y. (2022). Quantum delegated computing ciphertext retrieval scheme. Journal of Applied Physics, 131(4), Article 044401. https://doi.org/10.1063/5.0080097
Maiolo, T. A. C., Della Sala, F., Martina, L., & Soliani, G. (2006). Entanglement of electrons in interacting molecules. Theoretical and Mathematical Physics, 152(2), 1184–1191. https://doi.org/10.1007/s11232-007-0098-9
Malavolta, G., & Wahler, M. (2023). Non-interactive quantum key distribution. IACR Cryptology ePrint Archive, 2023, Article 618. https://doi.org/10.48550/arXiv.2304.02999
Mastriani, M. (2023). Multi-qubit teleportation and multi-bit superdense coding via cascade splitting. Optical and Quantum Electronics, 55(11), Article 1026. https://doi.org/10.1007/s11082-023-05295-8
Melnikov, D., Mironov, A., Mironov, S., Morozov, A., & Morozov, A. (2019). From topological to quantum entanglement. Journal of High Energy Physics, 2019(5), Article 116. https://doi.org/10.1007/JHEP05(2019)116
Melucci, M. (2013). Deriving a quantum information retrieval basis. The Computer Journal, 56(11), 1279–1291. https://doi.org/10.1093/comjnl/bxs095
Melucci, M. (2015). Elements of information retrieval. In Introduction to information retrieval and quantum modeling (pp. 11–32). Springer. https://doi.org/10.1007/978-3-662-48313-8_1
Melvin, T. (2023). Mechanizing quantum error correction through entangled quantum machine learning techniques. In Quantum computers: From fundamentals to technology. IntechOpen. https://doi.org/10.5772/intechopen.1002876
Mizukami, K., & Koga, A. (2023). Quantum algorithm for the microcanonical thermal pure quantum state method. Physical Review A, 108(1), Article 012404. https://doi.org/10.1103/PhysRevA.108.012404
Muralidharan, S., & Panigrahi, P. K. (2008). Perfect teleportation, quantum-state sharing, and superdense coding through a genuinely entangled five-qubit state. Physical Review A, 77(3), Article 032321. https://doi.org/10.1103/PhysRevA.77.032321
Naskar, S. (2023). Quantum algorithm for researching the nearest (QARN). arXiv. https://doi.org/10.48550/arXiv.2304.10976
Nema, A., Maity, A. G., Strelchuk, S., & Elkouss, D. (2023). Noise is resource-contextual in quantum communication. arXiv. https://doi.org/10.48550/arXiv.2305.00680
Nguyen, T., Paik, I., & Thang, T. (2022). Multi-feature machine learning with quantum superposition. In 2022 IEEE International Conference on Consumer Electronics-Asia (ICCE-Asia) (pp. 1–4). IEEE. https://doi.org/10.1109/ICCE-Asia57006.2022.9954778
Nielsen, M. A. (2000). Quantum information theory. arXiv. https://doi.org/10.48550/arXiv.quant-ph/0011036
Nielsen, M. A., & Chuang, I. L. (2010). Quantum computation and quantum information (10th anniversary ed.). Cambridge University Press.
Niknamian, S., Zaminpira, S., & Seneff, S. (2019). Quantum entanglement in theoretical physics as a new insight into cancer biology. viXra.
Noh, K., Pirandola, S., & Jiang, L. (2020). Enhanced energy-constrained quantum communication over bosonic Gaussian channels. Nature Communications, 11(1), Article 457. https://doi.org/10.1038/s41467-020-14329-6
Ohya, M., & Watanabe, N. (2010). Quantum entropy and its applications to quantum communication and statistical physics. Entropy, 12(5), 1194–1245. https://doi.org/10.3390/e12051194
Oszmaniec, M., Grudka, A., Horodecki, M., & Wójcik, A. (2016). Creating a superposition of unknown quantum states. Physical Review Letters, 116(11), Article 110403. https://doi.org/10.1103/PhysRevLett.116.110403
Pavličko, J., & Ziman, M. (2022). Robustness of optimal probabilistic storage and retrieval of unitary channels to noise. arXiv. https://doi.org/10.48550/arXiv.2211.07079
Penchev, V. (2020). Main concepts in philosophy of quantum information. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.3630828
Perlner, R., & Liu, Y.-K. (2017). Thermodynamic analysis of classical and quantum search algorithms. arXiv. https://doi.org/10.48550/arXiv.1709.10510
Piwowarski, B., Frommholz, I., Lalmas, M., & van Rijsbergen, K. (2010). What can quantum theory bring to information retrieval. In Proceedings of the 19th ACM International Conference on Information and Knowledge Management (CIKM) (pp. 59–68). ACM. https://doi.org/10.1145/1871437.1871450
Polzik, E. (2002). Atomic entanglement on a grand scale. Physics World, 15(9), Article 30. https://doi.org/10.1088/2058-7058/15/9/30
Rahmi, M., Shamanta, D., & Tasnim, A. (2012). Basic quantum algorithms and applications. International Journal of Computer Applications, 56(4), 26–31. https://doi.org/10.5120/8880-2868
Ralescu, A., & Mayfield, L. (2005). Generalization of common gates for quantum computation. In NAFIPS 2005 - 2005 Annual Meeting of the North American Fuzzy Information Processing Society (pp. 509–514). IEEE. https://doi.org/10.1109/NAFIPS.2005.1548607
Saha, D., & Panigrahi, P. K. (2012). N-qubit quantum teleportation, information splitting and superdense coding through the composite GHZ–Bell channel. Quantum Information Processing, 11(2), 615–628. https://doi.org/10.1007/s11128-011-0270-x
Schumacher, B., & Nielsen, M. A. (1996). Quantum data processing and error correction. Physical Review A, 54(4), 2629–2635. https://doi.org/10.1103/PhysRevA.54.2629
Shrivastava, P., Soni, K. K., & Rasool, A. (2019). Evolution of quantum computing based on Grover's search algorithm. In 2019 10th International Conference on Computing, Communication and Networking Technologies (ICCCNT) (pp. 1–6). IEEE. https://doi.org/10.1109/ICCCNT45670.2019.8944676
Sinha, S. (2023). Effect of quantum information scrambling on bound entangled states. arXiv. https://doi.org/10.48550/arXiv.2311.16209
Slepoy, A. (2006). Quantum gate decomposition algorithms (Report No. SAND2006-6962). Sandia National Laboratories. https://doi.org/10.2172/889415
Song, J., Lu, B., Liu, L., & Wang, C. (2023). Noisy quantum channel characterization using quantum neural networks. Electronics, 12(11), Article 2430. https://doi.org/10.3390/electronics12112430
Song, S. H., Le Gall, F., & Hayashi, M. (2023). Prior entanglement exponentially improves one-server quantum private information retrieval for quantum messages. arXiv. https://doi.org/10.48550/arXiv.2305.15875
Song, S., & Hayashi, M. (2021). Quantum private information retrieval for quantum messages. In 2021 IEEE International Symposium on Information Theory (ISIT) (pp. 1260–1265). IEEE. https://doi.org/10.1109/ISIT45174.2021.9517794
Taghizadeh Kourayem, F., Kabaranzad Ghadim, M., & Mousavi, S. A. A. (2026). Using dynamic selectors and artificial intelligence to harden web data retrieval codes. Knowledge Retrieval and Semantic Systems, 13(46), 1–24. https://doi.org/10.22054/jks.2026.89870.1753 [In Persian]
Techateerawat, P. (2012). Network management system for quantum key distribution. In 2012 Ninth International Conference on Information Technology - New Generations (pp. 415–420). IEEE. https://doi.org/10.1109/ITNG.2012.58
Terhal, B. M. (2015). Quantum error correction for quantum memories. Reviews of Modern Physics, 87(2), 307–346. https://doi.org/10.1103/RevModPhys.87.307
Tsallis, C. (2022). Entropy. In Thermodynamic weirdness (pp. 11–24). MIT Press. https://doi.org/10.7551/mitpress/11924.003.0011
Tunkelang, D., & Thelwall, M. (2009). Faceted search (Synthesis Lectures on Information Concepts, Retrieval, and Services). Morgan & Claypool Publishers.
Uprety, S., Gkoumas, D., & Song, D. (2021). A survey of quantum theory inspired approaches to information retrieval. ACM Computing Surveys, 53(5), 1–38. https://doi.org/10.1145/3402179
Uttam, S. (2012). Quantum information theory. In Quantum information processing and quantum error correction (pp. 457–492). Elsevier. https://doi.org/10.1016/B978-0-12-385491-9.00012-5
Van Rijsbergen, C. J. K. (2011). What is quantum information retrieval? In G. Amati & F. Crestani (Eds.), Advances in information retrieval theory (Vol. 6931, p. 2). Springer. https://doi.org/10.1007/978-3-642-23318-0_2
Wang, X. (2021). Quantum entanglement results from quantum state transition at fast-than-light speed with matter wave's phase velocity. Physical Science & Biophysics Journal, 5(2), 1–4. https://doi.org/10.23880/psbj-16000179
Wang, X. M. (2019). Entropy gain and information loss by measurements. arXiv. https://doi.org/10.48550/arXiv.1908.10364
Wilde, M. M. (2013). Quantum information and entropy. In Quantum information theory (pp. 252–291). Cambridge University Press. https://doi.org/10.1017/CBO9781139525343.012
Wong, B. (2020). On quantum entanglement. viXra.
Wootton, J. (2024). Circuit model of quantum computation. In Oxford research encyclopedia of physics. Oxford University Press. https://doi.org/10.1093/acrefore/9780190871994.013.30
Xue, Y. (2021). Basic theory of quantum entanglement and the possibility of passing on information faster than the speed of light. IOP Conference Series: Earth and Environmental Science, 658(1), Article 012001. https://doi.org/10.1088/1755-1315/658/1/012001
Yang, Y. G., Yang, P. Z., Xu, G. B., Zhou, Y. H., & Shi, W. M. (2023). Quantum private information retrieval over a collective noisy channel. Modern Physics Letters A, 38(01), 2350001. https://doi.org/10.1142/S0217732323500013
Zeilinger, A. (1998). Quantum entanglement: A fundamental concept finding its applications. Physica Scripta, 1998(T76), 203–209. https://doi.org/10.1238/Physica.Topical.076a00203
Zhan, Y.-B., Zhang, L.-L., & Zhang, Q.-Y. (2009). Quantum secure direct communication by entangled qutrits and entanglement swapping. Optics Communications, 282(23), 4633–4636. https://doi.org/10.1016/j.optcom.2009.08.024
Zhao, Y. (2023). Benchmarking machine learning models for quantum error correction. arXiv. https://doi.org/10.48550/arXiv.2311.11167
Zhao, Y., & Liu, D. (2023). Lattice gauge theory and topological quantum error correction with quantum deviations in the state preparation and error detection. Research Square. https://doi.org/10.21203/rs.3.rs-2615571/v1
Zuccon, G., & Azzopardi, L. (2010). Using the quantum probability ranking principle to rank interdependent documents. In C. Gurrin et al. (Eds.), Advances in information retrieval (Vol. 5993, pp. 357–369). Springer. https://doi.org/10.1007/978-3-642-12275-0_32