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
[1]
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.
[5]
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.
[6]
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.
[7]
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
Index terms have been assigned to the content through auto-classification.
Recommendations
Generalized Quantum Arthur--Merlin Games
This paper investigates the role of interaction and coins in quantum Arthur--Merlin games (also called public-coin quantum interactive proof systems). While the existing model restricts the messages from the verifier to be classical even in the quantum ...
Complexity Classification of Local Hamiltonian Problems
The calculation of ground-state energies of physical systems can be formalized as the $k$-local Hamiltonian problem, which is a natural quantum analogue of classical constraint satisfaction problems. One way of making the problem more physically meaningful ...
Quantum Free Games
STOC 2023: Proceedings of the 55th Annual ACM Symposium on Theory of ComputingThe complexity of free games with two or more classical players was essentially settled by Aaronson, Impagliazzo, and Moshkovitz (CCC’14). In the quantum world, there are two complexity classes that can be considered quantum analogues of classical ...
Comments
Information & Contributors
Information
Published In
DOI:10.1137/smjcat.49.6
Issue’s Table of Contents© 2020, Society for Industrial and Applied Mathematics.
Publisher
Society for Industrial and Applied Mathematics
United States
Publication History
Published: 01 January 2020
Author Tags
Author Tags
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 10 Nov 2024
Other Metrics
Citations
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
View Options
View options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in