Quantum Merlin-Arthur with an internally separable proof

TL;DR

This paper introduces a modified version of QMA where two unentangled proofs are strictly more powerful than one, under certain complexity assumptions, by leveraging a novel form of multipartite unentanglement.

Contribution

It proposes a new variant of QMA with an internally separable proof structure, providing a pathway to equate QMA(2) with NEXP under complexity assumptions.

Findings

Two unentangled proofs are more powerful than one proof assuming EXP ≠ NEXP.

The modification introduces a form of multipartite unentanglement in proofs.

This approach overcomes limitations of previous methods for relating QMA(2) and NEXP.

Abstract

We find a modification to QMA where having one quantum proof is strictly less powerful than having two unentangled proofs, assuming EXP $\ne$ NEXP. This gives a new route to prove QMA(2) = NEXP that overcomes the primary drawback of a recent approach [arXiv:2402.18790 , arXiv:2306.13247] (QIP 2024). Our modification endows each proof with a form of *multipartite* unentanglement: after tracing out one register, a small number of qubits are separable from the rest of the state.