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Non-interactive zero-knowledge arguments for QMA, with preprocessing

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Zero-knowledge proofs are one of the cornerstones of modern cryptography. It is well known that any language in NP admits a zero-knowledge proof. In the quantum setting, it is possible to go beyond NP. Zero-knowledge proofs for QMA have first been studied in a work of Broadbent et al (FOCS'16). There, the authors show that any language in QMA has an (interactive) zero-knowledge proof. In this talk, I will describe an idea, based on quantum teleportation, to remove interaction at the cost of adding an instance-independent preprocessing step. Assuming the Learning With Errors problem is hard for quantum computers, the resulting protocol is a non-interactive zero-knowledge argument for QMA, with a preprocessing step that consists of (i) the generation of a Common Reference String and (ii) a single (instance-independent) quantum message from the verifier to the prover.

This is joint work with Thomas Vidick and Tina Zhang