Shorter unentangled proofs for Ground State Connectivity

TL;DR

This paper demonstrates that for a quantum problem related to ground state connectivity, it is possible to significantly shorten the proof size using a two-prover unentangled protocol, with only a small reduction in the proof's reliability.

Contribution

The authors introduce a method to reduce the proof length for the Ground State Connectivity problem from superlinear to near-linear size using a two-copy unentangled proof in QMA(2).

Findings

Proof length reduced to order n with logarithmic factors.

Completeness-soundness gap becomes a small inverse polynomial in n.

Protocol maintains unentanglement with only minor reliability loss.

Abstract

Can one considerably shorten a proof for a quantum problem by using a protocol with a constant number of unentangled provers? We consider a frustration-free variant of the QCMA-complete Ground State Connectivity (GSCON) problem for a system of size n with a proof of superlinear-size. We show that we can shorten this proof in QMA(2): there exists a two-copy, unentangled proof with length of order n, up to logarithmic factors, while the completeness-soundness gap of the new protocol becomes a small inverse polynomial in n.