  Recently Chen and Movassagh proposed the quantum Merkle tree, which is a
quantum analogue of the well-known classical Merkle tree. It gives a succinct
verification protocol for quantum state commitment. Although they only proved
security against semi-honest provers, they conjectured its general security.
Using the proposed quantum Merkle tree, they gave a quantum analogue of
Kilian's succinct argument for NP, which is based on probabilistically
checkable proofs (PCPs). A nice feature of Kilian's argument is that it can be
extended to a zero-knowledge succinct argument for NP, if the underlying PCP is
zero-knowledge. Hence, a natural question is whether one can also make the
quantum succinct argument by Chen and Movassagh zero-knowledge as well. This
work makes progress on this problem. We generalize the recent result of
Broadbent and Grilo to show that any local quantum verifier can be made
simulable with a minor reduction in completeness and soundness. Roughly
speaking, a local quantum verifier is simulable if in the yes case, the local
views of the verifier can be computed without knowing the actual quantum proof;
it can be seen as the quantum analogue of the classical zero-knowledge PCPs.
Hence we conjecture that applying the proposed succinct quantum argument of
Chen and Movassagh to a simulable local verifier is indeed zero-knowledge.
