Zero-knowledge proofs are a fundamental building block in classical Cryptography, having far-reaching applications. Recently, there has been some effort in improving our understanding of Zero-knowledge for quantum complexity classes, that will hopefully lead us to striking objects as in the classical case. The goal of this talk is to give an overview of some of such results, in particular: All multi-prover system with entangled provers protocols can be made ZK; Simpler ZK protocols for QMA (which includes the first Proof of Knowledge ZK protocol and the first Non-interactive ZK protocol in the secret parameters model). Such results are achieved through new tools, namely Simulatable codes, QMA-completeness (under standard Karp reductions) of Consistency of Local Density Matrices and Simulatable proofs, that could be useful in different contexts. This talk is based on a joint work with William Slofstra and Henry Yuen, and on a joint work with Anne Broadbent.
