A Cryptographic Test of Quantumness and Certifiable Randomness from a Single Quantum Device

We consider a new model for the testing of untrusted quantum devices, consisting of a single polynomial time bounded quantum device interacting with a classical polynomial time verifier. In this model, we propose solutions to two tasks-a protocol for efficient classical verification that the untrusted device is "truly quantum" and a protocol for producing certifiable randomness from a single untrusted quantum device. Our solution relies on the existence of a new cryptographic primitive for constraining the power of an untrusted quantum device: post-quantum secure trapdoor claw-free functions that must satisfy an adaptive hardcore bit property. We show how to construct this primitive based on the hardness of the learning with errors (LWE) problem.