Quantum interactive proofs with short messages
Name
v007a007.pdf
Size
248.59 KB
Format
Adobe PDF
Checksum (MD5)
e20cdabb635360adf26c2405e6c0dc97
Author(s)
Beigi, Salman
Shor, Peter W.
Watrous, John
Date Issued
2011
Journal
Theory of computing
Publisher
Theory of Computing
Citation
Beigi, Salman, Peter Shor, and John Watrous, "Quantum interactive proofs with short messages." Theory of computing 7 (2011): no. 7 url http://www.theoryofcomputing.org/articles/v007a007/ ©2011 Author(s)
Version
Final published version
Abstract
This paper considers three variants of quantum interactive proof systems in which short (meaning logarithmic-length) messages are exchanged between the prover and verifier. The first variant is one in which the verifier sends a short message to the prover, and the prover responds with an ordinary, or polynomial-length, message; the second variant is one in which any number of messages can be exchanged, but where the combined length of all the messages is logarithmic; and the third variant is one in which the verifier sends polynomially many random bits to the prover, who responds with a short quantum message. We prove that in all of these cases the short messages can be eliminated without changing the power of the model, so the first variant has the expressive power of QMA and the second and third variants have the expressive power of BQP. These facts are proved through the use of quantum state tomography, along with the finite quantum de Finetti theorem for the first variant. ©2011
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
http://www.theoryofcomputing.org/articles/v007a007/
