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I'm wondering about a specific proof for Consistency of Local Density Matrices (CLDM) $ \in $ QMA appearing in "QMA-hardness of Consistency of Local Density Matrices with Applications to Quantum Zero-Knowledge". Arxiv link: https://arxiv.org/pdf/1911.07782.pdf#page=18&zoom=100,96,265.

The link should point directly to Lemma 3.3 on page 18.

In the soundness section, The authors assume that the candidate given by the prover is a product state. As far as I know, in the QMA settings, such an assumption can't be made. What do I miss? Does the concentration argument still work even when the given states are entangled? Thanks.

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    $\begingroup$ Consider spelling out CLDM; and please be more specific about which part of the paper exactly you are referring to. $\endgroup$
    – Norbert Schuch
    Commented Dec 17, 2023 at 13:22

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