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Quantum proof systems for iterated exponential time, and beyond

Authors:

Joseph Fitzsimons,

Henry YuenAuthors Info & Claims

STOC 2019: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

Pages 473 - 480

https://doi.org/10.1145/3313276.3316343

Published: 23 June 2019 Publication History

Abstract

We show that any language solvable in nondeterministic time exp( exp(⋯exp(n))), where the number of iterated exponentials is an arbitrary function R(n), can be decided by a multiprover interactive proof system with a classical polynomial-time verifier and a constant number of quantum entangled provers, with completeness 1 and soundness 1 − exp(−Cexp(⋯exp(n))), where the number of iterated exponentials is R(n)−1 and C>0 is a universal constant. The result was previously known for R=1 and R=2; we obtain it for any time-constructible function R.

The result is based on a compression technique for interactive proof systems with entangled provers that significantly simplifies and strengthens a protocol compression result of Ji (STOC’17). As a separate consequence of this technique we obtain a different proof of Slofstra’s recent result on the uncomputability of the entangled value of multiprover games (Forum of Mathematics, Pi 2019).

Finally, we show that even minor improvements to our compression result would yield remarkable consequences in computational complexity theory and the foundations of quantum mechanics: first, it would imply that the class MIP* contains all computable languages; second, it would provide a negative resolution to a multipartite version of Tsirelson’s problem on the relation between the commuting operator and tensor product models for quantum correlations.

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Cited By

Volčič J(2024)Constant-sized self-tests for maximally entangled states and single projective measurementsQuantum10.22331/q-2024-03-21-12928(1292)Online publication date: 21-Mar-2024
https://doi.org/10.22331/q-2024-03-21-1292
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
https://dl.acm.org/doi/10.1145/3618260.3649702
Mančinska LPrakash JSchafhauser C(2024)Constant-Sized Robust Self-Tests for States and Measurements of Unbounded DimensionCommunications in Mathematical Physics10.1007/s00220-024-05122-3405:9Online publication date: 31-Aug-2024
https://doi.org/10.1007/s00220-024-05122-3
Show More Cited By

Index Terms

Quantum proof systems for iterated exponential time, and beyond
1. Theory of computation
  1. Computational complexity and cryptography
    1. Quantum complexity theory

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cover image ACM Conferences

STOC 2019: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

June 2019

1258 pages

ISBN:9781450367059

DOI:10.1145/3313276

General Chair:
Moses Charikar
Stanford University
,
Program Chair:
Edith Cohen
Google, USA / Tel Aviv University, Israel

Copyright © 2019 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Association for Computing Machinery

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Publication History

Published: 23 June 2019

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Research-article

Funding Sources

Singapore?s Ministry of Education and National Research Foundation
US Air Force
NSF Physics Frontiers Center
US Air Force Office of Scientific Researc
National Science Foundation
Gordon and Betty Moore Foundation
Singapore National Research Foundation

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STOC '19

Sponsor:

SIGACT

STOC '19: 51st Annual ACM SIGACT Symposium on the Theory of Computing

June 23 - 26, 2019

AZ, Phoenix, USA

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Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

Volčič J(2024)Constant-sized self-tests for maximally entangled states and single projective measurementsQuantum10.22331/q-2024-03-21-12928(1292)Online publication date: 21-Mar-2024
https://doi.org/10.22331/q-2024-03-21-1292
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
https://dl.acm.org/doi/10.1145/3618260.3649702
Mančinska LPrakash JSchafhauser C(2024)Constant-Sized Robust Self-Tests for States and Measurements of Unbounded DimensionCommunications in Mathematical Physics10.1007/s00220-024-05122-3405:9Online publication date: 31-Aug-2024
https://doi.org/10.1007/s00220-024-05122-3
Mančinska LSchmidt S(2023)Counterexamples in self-testingQuantum10.22331/q-2023-07-11-10517(1051)Online publication date: 11-Jul-2023
https://doi.org/10.22331/q-2023-07-11-1051
Fu H(2022)Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimensionQuantum10.22331/q-2022-01-03-6146(614)Online publication date: 3-Jan-2022
https://doi.org/10.22331/q-2022-01-03-614
Mousavi HNezhadi SYuen HLeonardi SGupta A(2022)Nonlocal games, compression theorems, and the arithmetical hierarchyProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3519949(1-11)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3519949
Cui DMehta AMousavi HNezhadi S(2020)A generalization of CHSH and the algebraic structure of optimal strategiesQuantum10.22331/q-2020-10-21-3464(346)Online publication date: 21-Oct-2020
https://doi.org/10.22331/q-2020-10-21-346
Natarajan AWright J(2019)NEEXP is Contained in MIP*2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2019.00039(510-518)Online publication date: Nov-2019
https://doi.org/10.1109/FOCS.2019.00039

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