Quantum Merlin-Arthur Proof Systems: Are Multiple Merlins More Helpful to Arthur?

Details Quantum Merlin-Arthur Proof Systems: Are Multiple Merlins More Helpful to Arthur? Quantum Merlin-Arthur Proof Systems: Are Multiple Merlins More Helpful to Arthur?

2003-06-06

arxiv.org/abs/quant-ph/0306051v2

Conference version in Algorithms and Computation, 14th International Symposium, ISAAC 2003, volume 2906 of Lecture Notes in Co

Physics

Quantum Physics

LaTeX2e, 18 pages. The main statement (the condition under which QMA(k) = QMA(2)) is improved. The same improvement is done in

Scientific paper

This paper introduces quantum ``multiple-Merlin''-Arthur proof systems in which Arthur receives multiple quantum proofs that are unentangled with each other. Although classical multi-proof systems are obviously equivalent to classical single-proof systems (i.e., usual Merlin-Arthur proof systems), it is unclear whether or not quantum multi-proof systems collapse to quantum single-proof systems (i.e., usual quantum Merlin-Arthur proof systems). This paper presents a necessary and sufficient condition under which the number of quantum proofs is reducible to two. It is also proved that, in the case of perfect soundness, using multiple quantum proofs does not increase the power of quantum Merlin-Arthur proof systems.

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