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

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., standard Merlin-Arthur proof systems), it is unclear whether or not quantum multi-proof systems collapse to quantum single-proof systems (i.e., standard quantum MerlinArthur proof systems). This paper presents a way of reducing the number of proofs to two while keeping the two-sided bounded-error property, which gives 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. ∗ A preliminary version of this paper has appeared in Algorithms and Computation, 14th International Symposium, ISAAC 2003, volume 2906 of Lecture Notes in ...

• Type: Conference
• Year: 2003
• Where: ISAAC
• Authors: Hirotada Kobayashi, Keiji Matsumoto, Tomoyuki Yamakami
• Keywords: ISAAC 2003, Proof Systems, Quantum, Quantum Proofs