One-Shot Hybrid State Redistribution

Eyuri Wakakuwa1,2, Yoshifumi Nakata3,4,5, and Min-Hsiu Hsieh6,7

1Department of Communication Engineering and Informatics, Graduate School of Informatics and Engineering, The University of Electro-Communications, Tokyo 182-8585, Japan
2Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
3Yukawa Institute for Theoretical Physics, Kyoto university, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto, 606-8502, Japan
4Photon Science Center, Graduate School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
5JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan
6Centre for Quantum Software & Information (UTS:QSI), University of Technology Sydney, Sydney NSW, Australia
7Hon Hai (Foxconn) Research Institute, Taipei, Taiwan

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We consider state redistribution of a "hybrid" information source that has both classical and quantum components. The sender transmits classical and quantum information at the same time to the receiver, in the presence of classical and quantum side information both at the sender and at the decoder. The available resources are shared entanglement, and noiseless classical and quantum communication channels. We derive one-shot direct and converse bounds for these three resources, represented in terms of the smooth conditional entropies of the source state. Various coding theorems for two-party source coding problems are systematically obtained by reduction from our results, including the ones that have not been addressed in previous literature.

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Cited by

[1] Eyuri Wakakuwa and Yoshifumi Nakata, "One-Shot Triple-Resource Trade-Off in Quantum Channel Coding", IEEE Transactions on Information Theory 69 4, 2400 (2023).

[2] Ian George, Min-Hsiu Hsieh, and Eric Chitambar, 2023 IEEE International Symposium on Information Theory (ISIT) 96 (2023) ISBN:978-1-6654-7554-9.

[3] Xiaomin Liu, Zhengjun Xi, and Heng Fan, "Slepian–Wolf coding with quantum side information", Quantum Information Processing 22 11, 407 (2023).

[4] Manideep Mamindlapally and Andreas Winter, "Singleton Bounds for Entanglement-Assisted Classical and Quantum Error Correcting Codes", IEEE Transactions on Information Theory 69 9, 5857 (2023).

[5] Eyuri Wakakuwa and Yoshifumi Nakata, "One-Shot Randomized and Nonrandomized Partial Decoupling", Communications in Mathematical Physics 386 2, 589 (2021).

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