research-article

Stronger methods of making quantum interactive proofs perfectly complete

Authors:

Hirotada Kobayashi,

François Le Gall,

Harumichi NishimuraAuthors Info & Claims

ITCS '13: Proceedings of the 4th conference on Innovations in Theoretical Computer Science

Pages 329 - 352

https://doi.org/10.1145/2422436.2422475

Published: 09 January 2013 Publication History

Abstract

This paper presents stronger methods of achieving perfect completeness in quantum interactive proofs. First, it is proved that any problem in QMA has a two-message quantum interactive proof system of perfect completeness with constant soundness error, where the verifier has only to send a constant number of halves of EPR pairs. This in particular implies that the class QMA is necessarily included by the class QIP₁(2)} of problems having two-message quantum interactive proofs of perfect completeness, which gives the first nontrivial upper bound for QMA in terms of quantum interactive proofs. It is also proved that any problem having an $m$-message quantum interactive proof system necessarily has an ${(m+1)}$-message quantum interactive proof system of perfect completeness. This improves the previous result due to Kitaev and Watrous, where the resulting system of perfect completeness requires ${m+2}$ messages if not using the parallelization result.

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Cited By

Vidick TWatrous J(2018)Quantum ProofsFoundations and Trends® in Theoretical Computer Science10.1561/040000006811:1-2(1-215)Online publication date: 13-Dec-2018
https://dl.acm.org/doi/10.1561/0400000068
Grilo AKerenidis ISikora J(2015)QMA with Subset State WitnessesMathematical Foundations of Computer Science 201510.1007/978-3-662-48054-0_14(163-174)Online publication date: 11-Aug-2015
https://doi.org/10.1007/978-3-662-48054-0_14
Gosset DNagaj D(2013)Quantum 3-SAT Is QMA1-CompleteProceedings of the 2013 IEEE 54th Annual Symposium on Foundations of Computer Science10.1109/FOCS.2013.86(756-765)Online publication date: 26-Oct-2013
https://dl.acm.org/doi/10.1109/FOCS.2013.86

Index Terms

Stronger methods of making quantum interactive proofs perfectly complete
1. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Models of computation
    1. Interactive computation

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cover image ACM Conferences

ITCS '13: Proceedings of the 4th conference on Innovations in Theoretical Computer Science

January 2013

594 pages

ISBN:9781450318594

DOI:10.1145/2422436

Program Chair:
Robert Kleinberg
Cornell University

Copyright © 2013 ACM.

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Published: 09 January 2013

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ITCS '13: Innovations in Theoretical Computer Science

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Cited By

Vidick TWatrous J(2018)Quantum ProofsFoundations and Trends® in Theoretical Computer Science10.1561/040000006811:1-2(1-215)Online publication date: 13-Dec-2018
https://dl.acm.org/doi/10.1561/0400000068
Grilo AKerenidis ISikora J(2015)QMA with Subset State WitnessesMathematical Foundations of Computer Science 201510.1007/978-3-662-48054-0_14(163-174)Online publication date: 11-Aug-2015
https://doi.org/10.1007/978-3-662-48054-0_14
Gosset DNagaj D(2013)Quantum 3-SAT Is QMA1-CompleteProceedings of the 2013 IEEE 54th Annual Symposium on Foundations of Computer Science10.1109/FOCS.2013.86(756-765)Online publication date: 26-Oct-2013
https://dl.acm.org/doi/10.1109/FOCS.2013.86

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