On quantum interactive proofs with short messages

TL;DR

This paper demonstrates that quantum interactive proof systems with short initial messages and polynomial-length final messages are computationally equivalent to the class QMA, resolving an open problem in quantum complexity theory.

Contribution

It proves that quantum interactive proofs with logarithmic short messages and polynomial final messages are equivalent to QMA, clarifying their computational power.

Findings

Short-message quantum interactive proofs equal QMA in power

Resolved an open problem in quantum complexity theory

Established equivalence between specific proof systems and QMA

Abstract

This paper proves one of the open problem posed by Beigi et al. in arXiv:1004.0411v2. We consider quantum interactive proof systems where in the beginning the verifier and prover send messages to each other with the combined length of all messages being at most logarithmic (in the input length); and at the end the prover sends a polynomial-length message to the verifier. We show that this class has the same expressive power as QMA.