Document Open Access Logo

Retracted: Two-Player Entangled Games are NP-Hard

Authors Anand Natarajan , Thomas Vidick

PDF
Thumbnail PDF

File

LIPIcs.CCC.2018.20.pdf
  • Filesize: 0.59 MB
  • 18 pages

Document Identifiers

Author Details

Anand Natarajan
  • Center for Theoretical Physics, MIT, Cambridge, USA
Thomas Vidick
  • Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, USA

Funding

  • Natarajan, Anand: Supported by NSF CAREER Grant CCF-1452616
  • Vidick, Thomas: Supported by NSF CAREER Grant CCF-1553477, AFOSR YIP award number FA9550-16-1-0495, and the IQIM, an NSF Physics Frontiers Center (NSF Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028).

Cite AsGet BibTex

Anand Natarajan and Thomas Vidick. Retracted: Two-Player Entangled Games are NP-Hard. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.CCC.2018.20

Abstract

The article, published on June 4th, 2018 in the CCC 2018 proceedings, has been retracted by agreement between the authors, the editor(s), and the publisher Schloss Dagstuhl / LIPIcs. The retraction has been agreed due to an error in the proof of the main result. This error is carried over from an error in the referenced paper “Three-player entangled XOR games are NP-hard to approximate” by Thomas Vidick (SICOMP ’16). That paper was used in an essential way to obtain the present result, and the error cannot be addressed through an erratum. See Retraction Notice on the last page of the PDF. We show that it is NP-hard to approximate, to within an additive constant, the maximum success probability of players sharing quantum entanglement in a two-player game with classical questions of logarithmic length and classical answers of constant length. As a corollary, the inclusion NEXP subseteq MIP^*, first shown by Ito and Vidick (FOCS'12) with three provers, holds with two provers only. The proof is based on a simpler, improved analysis of the low-degree test of Raz and Safra (STOC'97) against two entangled provers.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum complexity theory
  • Theory of computation → Interactive proof systems
  • Theory of computation → Complexity classes
Keywords
  • low-degree testing
  • entangled nonlocal games
  • multi-prover interactive proof systems

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, and Mario Szegedy. Proof verification and the hardness of approximation problems. J. ACM, 45(3):501-555, 1998. Google Scholar
  2. Sanjeev Arora and Shmuel Safra. Probabilistic checking of proofs: A new characterization of NP. J. ACM, 45(1):70-122, 1998. Google Scholar
  3. László Babai, Lance Fortnow, and Carsten Lund. Non-deterministic exponential time has two-prover interactive protocols. Computational Complexity, 1:3-40, 1991. Google Scholar
  4. John S. Bell. On the Einstein-Podolsky-Rosen paradox. Physics, 1:195-200, 1964. Google Scholar
  5. Manuel Blum, Michael Luby, and Ronitt Rubinfeld. Self-testing/correcting with applications to numerical problems. Journal of Computer and System Sciences, 47:549-595, 1993. Google Scholar
  6. Richard Cleve, Peter Høyer, Ben Toner, and John Watrous. Consequences and limits of nonlocal strategies. 2004. URL: http://arxiv.org/abs/quant-ph/0404076.
  7. Irit Dinur, David Steurer, and Thomas Vidick. A parallel repetition theorem for entangled projection games. Computational Complexity, 24(2):201-254, 2015. URL: http://dx.doi.org/10.1007/s00037-015-0098-3.
  8. Albert Einstein, Boris Podolsky, and Nathan Rosen. Can quantum-mechanical description of physical reality be considered complete? Physical review, 47(10):777, 1935. Google Scholar
  9. Uriel Feige, Shafi Goldwasser, Laszlo Lovász, Shmuel Safra, and Mario Szegedy. Interactive proofs and the hardness of approximating cliques. J. ACM, 43(2):268-292, 1996. Google Scholar
  10. Joseph Fitzsimons and Thomas Vidick. A multiprover interactive proof system for the local Hamiltonian problem. In Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science, pages 103-112. ACM, 2015. Google Scholar
  11. Shafi Goldwasser, Yael Tauman Kalai, and Guy N. Rothblum. Delegating computation: Interactive proofs for muggles. Journal of the ACM (JACM), 62(4):27, 2015. Google Scholar
  12. Johan Håstad. Some optimal inapproximability results. Journal of the ACM (JACM), 48(4):798-859, 2001. Google Scholar
  13. Tsuyoshi Ito, Hirotada Kobayashi, and Keiji Matsumoto. Oracularization and two-prover one-round interactive proofs against nonlocal strategies. In Proceedings: Twenty-Fourth Annual IEEE Conference on Computational Complexity (CCC 2009), pages 217-228, July 2009. Google Scholar
  14. Tsuyoshi Ito and Thomas Vidick. A multi-prover interactive proof for NEXP sound against entangled provers. Proc. 53rd FOCS, pages 243-252, 2012. URL: http://arxiv.org/abs/1207.0550.
  15. Rahul Jain, Zhengfeng Ji, Sarvagya Upadhyay, and John Watrous. QIP = PSPACE. Communications of the ACM, 53(12):102-109, 2010. URL: http://arxiv.org/abs/0907.4737.
  16. Zhengfeng Ji. Classical verification of quantum proofs. In Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, pages 885-898. ACM, 2016. Google Scholar
  17. Zhengfeng Ji. Compression of quantum multi-prover interactive proofs. 2016. URL: http://arxiv.org/abs/1610.03133.
  18. Yael Tauman Kalai, Ran Raz, and Ron D. Rothblum. How to delegate computations: the power of no-signaling proofs. In David B. Shmoys, editor, Symposium on Theory of Computing, STOC 2014, New York, NY, USA, May 31 - June 03, 2014, pages 485-494. ACM, 2014. URL: http://dx.doi.org/10.1145/2591796.2591809.
  19. Carsten Lund, Lance Fortnow, Howard Karloff, and Noam Nisan. Algebraic methods for interactive proof systems. Journal of the ACM (JACM), 39(4):859-868, 1992. Google Scholar
  20. Anand Natarajan and Thomas Vidick. A quantum linearity test for robustly verifying entanglement. In Hamed Hatami, Pierre McKenzie, and Valerie King, editors, Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017, Montreal, QC, Canada, June 19-23, 2017, pages 1003-1015. ACM, 2017. URL: http://dx.doi.org/10.1145/3055399.3055468.
  21. Anand Natarajan and Thomas Vidick. Low-degree testing for quantum states, and a quantum entangled games PCP. 2018. URL: http://arxiv.org/abs/1801.03821v2.
  22. Ran Raz and Shmuel Safra. A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP. In Frank Thomson Leighton and Peter W. Shor, editors, Proceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing, El Paso, Texas, USA, May 4-6, 1997, pages 475-484. ACM, 1997. URL: http://dx.doi.org/10.1145/258533.258641.
  23. Ben Reichardt, Falk Unger, and Umesh Vazirani. A classical leash for a quantum system: Command of quantum systems via rigidity of CHSH games. Nature, 496(7446):456-460, 2013. Google Scholar
  24. Adi Shamir. IP = PSPACE. J. ACM, 39(4):869-877, 1992. Google Scholar
  25. Ben Toner. Monogamy of non-local quantum correlations. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 465(2101):59-69, 2009. URL: http://dx.doi.org/10.1098/rspa.2008.0149.
  26. Thomas Vidick. Three-player entangled XOR games are NP-hard to approximate. In Proc. 54th FOCS, 2013. URL: http://arxiv.org/abs/1302.1242.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact