Quantum one-time tables for unconditionally secure qubit-commitment

Seok Hyung Lie1, Hyukjoon Kwon2, M. S. Kim2,3, and Hyunseok Jeong1

1Department of Physics and Astronomy, Seoul National University, Seoul, 151-742, Korea
2QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
3Korea Institute for Advanced Study, Seoul, 02455, Korea

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The commodity-based cryptography is an alternative approach to realize conventionally impossible cryptographic primitives such as unconditionally secure bit-commitment by consuming pre-established correlation between distrustful participants. A unit of such classical correlation is known as the one-time table (OTT). In this paper, we introduce a new example besides quantum key distribution in which quantum correlation is useful for cryptography. We propose a scheme for unconditionally secure qubit-commitment, a quantum cryptographic primitive forbidden by the recently proven no-masking theorem in the standard model, based on the consumption of the quantum generalization of the OTT, the bipartite quantum state we named $\textit{quantum one-time tables}$ (QOTT). The construction of the QOTT is based on the newly analyzed internal structure of quantum masker and the quantum secret sharing schemes. Our qubit-commitment scheme is shown to be universally composable. We propose to measure the randomness cost of preparing a (Q)OTT in terms of its entropy, and show that the QOTT with superdense coding can increase the security level with half the cost of OTTs for unconditionally secure bit-commitment. The QOTT exemplifies an operational setting where neither maximally classically correlated state nor maximally entangled state, but rather a well-structured partially entangled mixed state is more valuable resource.

A well-prepared correlation can make conventionally impossible cryptographic primitives. For example, a probability distribution called `one-time table' allows the implementation of unconditionally secure bit-commitment. In this work, the authors generalize this commodity-based cryptography to the quantum realm and suggest the quantum one-time table for unconditionally secure qubit-commitment. It is shown that quantum randomness can achieve the same level of security with half the entropy of its classical counterpart.

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Cited by

[1] Seok Hyung Lie and Hyunseok Jeong, "Randomness cost of masking quantum information and the information conservation law", Physical Review A 101 5, 052322 (2020).

[2] Mao-Sheng Li and Kavan Modi, "Probabilistic and approximate masking of quantum information", Physical Review A 102 2, 022418 (2020).

[3] Seok Hyung Lie, Seongjeon Choi, and Hyunseok Jeong, "The Min-entropy as a Resource for One-Shot Private State Transfer, Quantum Masking and State Transition", arXiv:2010.14796.

[4] Uzi Pereg, Christian Deppe, and Holger Boche, "Quantum Channel State Masking", arXiv:2006.05925.

[5] Huaixin Cao, Yuxing Du, Zhihua Guo, Kanyuan Han, and Chuan Yan, "Masking quantum information into a tripartite syste", arXiv:2004.14540.

[6] Huaixin Cao, Yuxing Du, Zhihua Guo, Kanyuan Han, and Chuan Yang, "Masking quantum information encoded in pure and mixed states", arXiv:2004.14572.

[7] Seok Hyung Lie and Hyunseok Jeong, "Randomness for quantum channels:Genericity of catalysis and quantum advantage of uniformness", arXiv:2010.14795.

[8] A. G. Abdelwahab, S. A. Ghwail, Nasser Metwally, M. H. Mahran, and A. -S. F. Obada, "The concealment of accelerated information is possible", Quantum Information Processing 20 2, 71 (2021).

[9] Seok Hyung Lie and Hyunsek Jeong, "Correlational Resource Theory of Catalytic Quantum Randomness under Conservation Law", arXiv:2104.00300.

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