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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 which 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.
Randomness plays a central rol in the quantum mechanical description of our interactions. We review the relationship between the violation of Bell inequalities, non signaling and randomness. We discuss the challenge in defining a random string, and s
Quantum information processing shows advantages in many tasks, including quantum communication and computation, comparing to its classical counterpart. The essence of quantum processing lies on the fundamental difference between classical and quantum
Quantum theory allows for randomness generation in a device-independent setting, where no detailed description of the experimental device is required. Here we derive a general upper bound on the amount of randomness that can be generated in such a se
In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e. it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an asymptotic proper
Randomness expansion where one generates a longer sequence of random numbers from a short one is viable in quantum mechanics but not allowed classically. Device-independent quantum randomness expansion provides a randomness resource of the highest se