Classical zero-knowledge arguments for quantum computations

Thomas Vidick1 and Tina Zhang2

1Department of Computing and Mathematical Sciences, California Institute of Technology, USA
2Division of Physics, Mathematics and Astronomy, California Institute of Technology, USA

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We show that every language in QMA admits a classical-verifier, quantum-prover zero-knowledge argument system which is sound against quantum polynomial-time provers and zero-knowledge for classical (and quantum) polynomial-time verifiers. The protocol builds upon two recent results: a computational zero-knowledge proof system for languages in QMA, with a quantum verifier, introduced by Broadbent et al. (FOCS 2016), and an argument system for languages in QMA, with a classical verifier, introduced by Mahadev (FOCS 2018).

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► References

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Cited by

[1] Gorjan Alagic, Andrew M. Childs, Alex B. Grilo, and Shih-Han Hung, Lecture Notes in Computer Science 12552, 153 (2020) ISBN:978-3-030-64380-5.

[2] Jose Carrasco, Andreas Elben, Christian Kokail, Barbara Kraus, and Peter Zoller, "Theoretical and Experimental Perspectives of Quantum Verification", PRX Quantum 2 1, 010102 (2021).

[3] Prabhanjan Ananth and Rolando L. La Placa, Lecture Notes in Computer Science 12552, 123 (2020) ISBN:978-3-030-64380-5.

[4] Andrea Coladangelo, Thomas Vidick, and Tina Zhang, Lecture Notes in Computer Science 12172, 799 (2020) ISBN:978-3-030-56876-4.

[5] Akihiro Mizutani, Yuki Takeuchi, Ryo Hiromasa, Yusuke Aikawa, and Seiichiro Tani, "Computational self-testing for entangled magic states", Physical Review A 106 1, L010601 (2022).

[6] Prabhanjan Ananth, Kai-Min Chung, and Rolando L. La Placa, Lecture Notes in Computer Science 12825, 346 (2021) ISBN:978-3-030-84241-3.

[7] Thomas Vidick and Tina Zhang, Lecture Notes in Computer Science 12697, 630 (2021) ISBN:978-3-030-77885-9.

[8] Anne Broadbent and Alex Bredariol Grilo, "QMA-Hardness of Consistency of Local Density Matrices with Applications to Quantum Zero-Knowledge", SIAM Journal on Computing 51 4, 1400 (2022).

[9] Gorjan Alagic, Andrew M. Childs, Alex B. Grilo, and Shih-Han Hung, "Non-interactive classical verification of quantum computation", arXiv:1911.08101, (2019).

[10] Andrea Coladangelo, Thomas Vidick, and Tina Zhang, "Non-interactive zero-knowledge arguments for QMA, with preprocessing", arXiv:1911.07546, (2019).

[11] Honghao Fu, Daochen Wang, and Qi Zhao, "Parallel self-testing of EPR pairs under computational assumptions", arXiv:2201.13430, (2022).

[12] Anne Broadbent, Arthur Mehta, and Yuming Zhao, "Quantum delegation with an off-the-shelf device", arXiv:2304.03448, (2023).

[13] Prabhanjan Ananth and Rolando L. La Placa, "Secure Quantum Extraction Protocols", arXiv:1911.07672, (2019).

[14] Eric Culf and Arthur Mehta, "New Approaches to Complexity via Quantum Graphs", arXiv:2309.12887, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-06-22 13:29:45) and SAO/NASA ADS (last updated successfully 2024-06-22 13:29:46). The list may be incomplete as not all publishers provide suitable and complete citation data.