Interactive Proofs with Quantum Finite Automata
Abstract
Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors initiated in 2004 a study on the computational power of quantum interactive proof systems whose verifiers are particularly limited to quantum finite automata. As a follow-up to the authors' early journal publication [J. Comput. System Sci., vol.75, pp.255-269, 2009], we further investigate the quantum nature of interactions between provers and verifiers by studying how various restrictions on quantum interactive proof systems affect the language recognition power of the proof systems. In particular, we examine three intriguing restrictions that (i) provers always behave in a classical fashion, (ii) verifiers always reveal to provers the information on next moves, and (iii) the number of interactions between provers and verifiers is bounded.
Keywords
Cite
@article{arxiv.1401.2929,
title = {Interactive Proofs with Quantum Finite Automata},
author = {Harumichi Nishimura and Tomoyuki Yamakami},
journal= {arXiv preprint arXiv:1401.2929},
year = {2015}
}
Comments
A4, 10pt, 2 figures, 20 pages. This paper is a complete version of the second half part of the extended abstract appearing in the Proc. of CIAA 2004, LNCS vol.3317, pp.225-236. A complete version of the first half had already appeared in JCSS, 2009. (*) Please note that there is a substantial text overlap with arXiv:quant-ph/0410040 as explained as above