Cited By
View all- Mastel KSlofstra WMohar BShinkar IO'Donnell R(2024)Two Prover Perfect Zero Knowledge for MIP*Proceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649702(991-1002)Online publication date: 10-Jun-2024
Erratum: : Three-Player Entangled XOR Games are NP-hard to Approximate
Abstract
This note indicates an error in the proof of Theorem 3.1 in [T. Vidick, SIAM J. Comput., 45 (2016), pp. 1007--1063]. Due to an induction step in the soundness analysis not being carried out correctly, the analysis fails to prove the claimed result. The error invalidates the proofs of the main computational hardness results claimed in the paper. We discuss implications for subsequent works. In some cases results can be partially recovered by applying a weakened version of Theorem 3.1 shown in [Z. Ji et al., Quantum Soundness of the Classical Low Individual Degree Test, arXiv:2009.1298, 2020] subsequently to the discovery of the error. The validity of Theorem 3.1 as stated in the paper remains an open question.
References
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L. Babai, L. Fortnow, and C. Lund, Non-deterministic exponential time has two-prover interactive protocols, Comput. Complexity, 1 (1991), pp. 3--40.
[2]
Z. Ji, A. Natarajan, T. Vidick, J. Wright, and H. Yuen, MIP$^*$= RE, preprint, arXiv:2001.04383v2, 2020.
[3]
Z. Ji, A. Natarajan, T. Vidick, J. Wright, and H. Yuen, Quantum Soundness of the Classical Low Individual Degree Test, manuscript, arXiv:2009.1298, 2020.
[4]
A. Natarajan and T. Vidick, Low-degree testing for quantum states, and a quantum entangled games PCP for QMA, in Proceedings of the 59th Annual Symposium on Foundations of Computer Science, IEEE, 2018, pp. 731--742.
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A. Natarajan and T. Vidick, Two-player entangled games are NP-hard, in Proceedings of the 33rd Computational Complexity Conference, Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018.
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A. Natarajan and J. Wright, NEEXP is contained in MIP$^*$, in Proceedings of the 60th Annual Symposium on Foundations of Computer Science, IEEE, 2019, pp. 510--518.
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R. Raz and S. Safra, A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP, in Proceedings of the 29th Annual ACM Symposium on Theory of Computing, ACM, New York, 1997, pp. 475--484.
[8]
T. Vidick, Three-player entangled XOR games are NP-hard to approximate, SIAM J. Comput., 45 (2016), pp. 1007--1063.
Index Terms
- Erratum: Three-Player Entangled XOR Games are NP-hard to Approximate
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DOI:10.1137/smjcat.49.6
Issue’s Table of Contents© 2020, Society for Industrial and Applied Mathematics.
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Society for Industrial and Applied Mathematics
United States
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Published: 01 January 2020
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View all- Mastel KSlofstra WMohar BShinkar IO'Donnell R(2024)Two Prover Perfect Zero Knowledge for MIP*Proceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649702(991-1002)Online publication date: 10-Jun-2024
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