Shorter unentangled proofs for ground state connectivity

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 $$\textsf {QCMA}$$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 $$\textsf {QMA}(2)$$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.

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