Document Type : Research Article
Authors
Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran
Abstract
In this paper, we want to investigate classical-quantum multiple access wiretap channels (CQ-MA-WTC) under one-shot setting. In this regard, we analyze the CQ-MA-WTC using a simultaneous position-based decoder for reliable decoding and using a newly introduced technique to decode securely. Also, for the sake of comparison, we analyze the CQ-MA-WTC using Sen’s one-shot joint typicality lemma for reliable decoding. The simultaneous position-based decoder tends to a multiple hypothesis testing problem. Also, using convex splitting to analyze the privacy criteria in a simultaneous scenario becomes
problematic. To overcome both problems, we first introduce a new channel that can be considered as a dual to the CQ-MA-WTC. This channel is called a point-to-point quantum wiretap channel with multiple messages (PP-QWTC). In the following, as a strategy to solve the problem, we also investigate and analyze quantum broadcast channels (QBC) in the one-shot regime.
Keywords
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[33] Mark M Wilde. Sequential decoding of a general classical-quantum channel. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 469(2157):20130259, 2013.
[2] Jon Yard, Patrick Hayden, and Igor Devetak. Quantum broadcast channels. IEEE Transactions on Information Theory, 57(10):7147–7162, 2011.
[3] Ivan Savov. Network information theory for classical-quantum channels. arXiv preprint arXiv:1208.4188, 2012.
[4] Abbas El Gamal and Young-Han Kim. Lecture notes on network information theory, 2010.
[5] Ning Cai, Andreas Winter, and Raymond W Yeung. Quantum privacy and quantum wiretap channels. problems of information transmission, 40(4):318–336, 2004.
[6] Igor Devetak. The private classical capacity and quantum capacity of a quantum channel. IEEE Transactions on Information Theory, 51(1):44–55, 2005.
[7] Omar Fawzi, Patrick Hayden, Ivan Savov, Pranab Sen, and Mark M Wilde. Classical communication over a quantum interference channel. IEEE Transactions on Information Theory, 58(6):3670–3691, 2012.
[8] Hadi Aghaee and Bahareh Akhbari. One-shot achievable secrecy rate regions for quantum interference wiretap channel. The ISC International Journal of Information Security (ISeCure), 14(3):71–80, 2022.
[9] Hadi Aghaee and Bahareh Akhbari. Classicalquantum multiple access wiretap channel. In 2019 16th International ISC (Iranian Society of Cryptology) Conference on Information Security and Cryptology (ISCISC), pages 99–103. IEEE, 2019.
[10] Hadi Aghaee and Bahareh Akhbari. Private classical information over a quantum multiple access channel: One-shot secrecy rate region. In 2020 10th International Symposium onTelecommunications (IST), pages 222–226. IEEE, 2020.
[11] Hadi Aghaee and Bahareh Akhbari. Classicalquantum multiple access channel with secrecy constraint: One-shot rate region. International Journal of Information and Communication Technology Research, 12(2):1–10, 2020.
[12] Hadi Aghaee and Bahareh Akhbari. Classicalquantum multiple access wiretap channel with common message: one-shot rate region. In 2020 11th International Conference on Information and Knowledge Technology (IKT), pages 55–61. IEEE, 2020.
[13] Hadi Aghaee and Bahareh Akhbari. Entanglement-assisted classical-quantum multiple access wiretap channel: One-shot achievable rate region. In 2022 30th International Conference on Electrical Engineering (ICEE), pages 693–699. IEEE, 2022.
[14] Pranab Sen. Unions, intersections and a oneshot quantum joint typicality lemma. S¯adhan¯a, 46(1):1–44, 2021.
[15] Aaron D Wyner. The wire-tap channel. Bell system technical journal, 54(8):1355–1387, 1975.
[16] Sayantan Chakraborty, Aditya Nema, and Pranab Sen. One-shot inner bounds for sending private classical information over a quantum mac. In 2021 IEEE Information Theory Workshop (ITW), pages 1–6. IEEE, 2021.
[17] Haoyu Qi, Qingle Wang, and Mark M Wilde. Applications of position-based coding to classical communication over quantum channels. Journal of Physics A: Mathematical and Theoretical, 51(44):444002, 2018.
[18] Anurag Anshu. One-shot protocols for communication over quantum networks: Achievability and limitations. PhD thesis, National University of Singapore (Singapore), 2018.
[19] Anurag Anshu, Rahul Jain, and Naqueeb Ahmad Warsi. A generalized quantum slepianwolf. IEEE Transactions on Information Theory, 64(3):1436–1453, 2017.
[20] R´emi A Chou. Private classical communication over quantum multiple-access channels. IEEE Transactions on Information Theory, 68(3):1782–1794, 2021.
[21] Mark M Wilde. Position-based coding and convex splitting for private communication over quantum channels. Quantum Information Processing, 16(10):1–35, 2017.
[22] Ligong Wang and Renato Renner. One-shot classical-quantum capacity and hypothesis testing. Physical Review Letters, 108(20):200501, 2012.
[23] Hisaharu Umegaki. Conditional expectation in an operator algebra, iv (entropy and information). In Kodai Mathematical Seminar Reports, volume 14, pages 59–85. Department of Mathematics, Tokyo Institute of Technology, 1962.
[24] Mario Berta, Matthias Christandl, and Renato Renner. The quantum reverse shannon theorem based on one-shot information theory. Communications in Mathematical Physics, 306(3):579–615,2011.
[25] Farzin Salek, Anurag Anshu, Min-Hsiu Hsieh, Rahul Jain, and Javier Rodr´ıguez Fonollosa. One-shot capacity bounds on the simultaneous transmission of classical and quantum information. IEEE Transactions on Information Theory, 66(4):2141–2164, 2019.
[26] Nikola Ciganovi´c, Normand J Beaudry, and Renato Renner. Smooth max-information as one-shot generalization for mutual information. IEEE Transactions on Information Theory, 60(3):1573–1581, 2013.
[27] Masahito Hayashi and Hiroshi Nagaoka. General formulas for capacity of classical-quantum channels. IEEE Transactions on Information Theory, 49(7):1753–1768, 2003.
[28] Farzin Salek, Anurag Anshu, Min-Hsiu Hsieh, Rahul Jain, and Javier R Fonollosa. One-shot capacity bounds on the simultaneous transmission of public and private information over quantum channels. In 2018 IEEE International Sympo-
sium on Information Theory (ISIT), pages 296–300. IEEE, 2018.
[29] Mark M Wilde, Marco Tomamichel, and Mario Berta. Converse bounds for private communication over quantum channels. IEEE Transactions on Information Theory, 63(3):1792–1817, 2017.
[30] Pranab Sen. Inner bounds via simultaneous decoding in quantum network information theory. S¯adhan¯a, 46(1):1–20, 2021.
[31] Mark M Wilde. Quantum information theory. Cambridge University Press, 2013.
[32] Ke Li. Discriminating quantum states: The multiple chernoff distance. The Annals of Statistics, 44(4):1661–1679, 2016.
[33] Mark M Wilde. Sequential decoding of a general classical-quantum channel. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 469(2157):20130259, 2013.
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