Cart (Loading....) | Create Account
Close category search window

Quantum information and the PCP theorem

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Raz, R. ; Weizmann Inst., Rehovot, Israel

Our main result is that the membership x ε SAT (for x of length n) can be proved by a logarithmic-size quantum state |Ψ>, together with a polynomial-size classical proof consisting of blocks of length polylog(n) bits each, such that after measuring the state |Ψ> the verifier only needs to read one block of the classical proof. This shows that if a short quantum witness is available then a (classical) PCP with only one query is possible. Our second result is that the class QIP/qpoly contains all languages. That is, for any language L (even non-recursive), the membership x ε L (for x of length n) can be proved by a polynomial-size quantum interactive proof, where the verifier is a polynomial-size quantum circuit with working space initiated with some quantum state |ΨL,n> (depending only on L and n). Moreover, the interactive proof that we give is of only one round, and the messages communicated are classical. The advice |ΨL,n> given to the verifier can also be replaced by a classical probabilistic advice, as long as this advice is kept as a secret from the proven Our result can hence be interpreted as: the class IP/rpoly contains all languages. For the proof of the second result, we introduce the quantum low-degree-extension of a string of bits. The main result requires an additional machinery of quantum low-degree-test.

Published in:

Foundations of Computer Science, 2005. FOCS 2005. 46th Annual IEEE Symposium on

Date of Conference:

23-25 Oct. 2005

Need Help?

IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.