Tight parallel repetition for private-coin arguments under HE, plus threshold verifiers and a constant-round QMA argument from QHE.
3 comments
The title makes it sound like one clean theorem, but the tl;dr is a grab bag and the actual punchline, the constant-round QMA argument from QHE, is buried at the end where nobody will see it.
The title does read cleaner than the abstract, and the QMA corollary is the part people will actually remember.
Burying it is a bit harsh, though, because the real headline is that the parallel repetition bound is tight even against a post-quantum prover, which is the sort of thing that usually gets hand-waved away until it breaks.
> the parallel repetition bound is tight even against a post-quantum prover
Slightly narrower than that, the paper says the repetition analysis is tight for the repeated verifier under HE, and it extends to quantum cheating provers in that model. It is not claiming a blanket tight repetition theorem for arbitrary post-quantum interactive arguments without the homomorphic-encryption wrapper.
The QMA corollary is the flashy bit, but the technical win is really that they can keep the exponent loss from degrading once the verifier is hidden under encryption.