ConstantSpace Quantum Interactive Proofs Against Multiple Provers
Abstract
We present upper and lower bounds of the computational complexity of the twoway communication model of multipleprover quantum interactive proof systems whose verifiers are limited to measuremany twoway quantum finite automata. We prove that (i) the languages recognized by those multipleprover systems running in expected polynomial time are exactly the ones in NEXP, the nondeterministic exponentialtime complexity class, (ii) if we further require verifiers to be oneway quantum automata, then their associated proof systems recognize contextfree languages but not beyond languages in NE, the nondeterministic linear exponentialtime complexity class, and moreover, (iii) when no time bound is imposed, the proof systems become as powerful as Turing machines. The first two results answer affirmatively an open question, posed by Nishimura and Yamakami [J. Comput. System Sci, 75, pp.255269, 2009], of whether multipleprover quantum interactive proof systems are more powerful than singleprover ones. Our proofs are simple and intuitive, although they heavily rely on an earlier result on multipleprover interactive proof systems of Feige and Shamir [J. Comput. System Sci., 44, pp.259271, 1992].
 Publication:

arXiv eprints
 Pub Date:
 September 2013
 DOI:
 10.48550/arXiv.1309.0429
 arXiv:
 arXiv:1309.0429
 Bibcode:
 2013arXiv1309.0429Y
 Keywords:

 Quantum Physics;
 Computer Science  Computational Complexity
 EPrint:
 A4, 10pt, 10 pages. The results of this paper were first reported at the 4th Central European Quantum Information Processing Workshop (CEQIS 2007), June 2427, 2007, Valtice, Czech Republic