Non-interactive Zero-Knowledge Arguments for QMA, with Preprocessing.

A non-interactive zero-knowledge (NIZK) proof system for a language \\(L\\in \\text {NP} \\) allows a prover (who is provided with an instance \\(x \\in L\\), and a witness w for x) to compute a classical certificate \\(\\pi \\) for the claim that \\(x\\in L\\) such that \\(\\pi \\) has the following properties: 1) \\(\\pi \\) can be verified efficiently, and 2) \\(\\pi \\) does not reveal any information about w, besides the fact that it exists (i.e. that \\(x \\in L\\)). NIZK proof systems have recently been shown to exist for all languages in \\(\\text {NP} \\) in the common reference string (CRS) model and under the learning with errors (LWE) assumption.