Effects of relaxed assumptions on semi-device-independent randomness expansion.

Semi-device-independent randomness expansion is the protocol which can generate and certify perfect free random numbers, without making detailed assumptions on the internal working of quantum devices, except the bound on the dimension of the Hilbert space. The two-dimensional (2D) quantum witness violation has been used to generate guaranteed fresh randomness from untrusted devices in the prepare-and-measure configuration. In this paper we first show that the 2D quantum witness violation can be simulated by a classical deterministic process by relaxing the assumption of the dimension. A deterministic process to simulate the generation of random numbers is given, under the hidden variables model, with just the high dimensional measurement device and one qubit communication. This makes the generated number essentially deterministic, which is said to be pseudorandom. Then we also show that when we relax the freedom of choice, there is the exact region for which quantum correlations can be simulated by the classical process in the task of randomness expansion. [ABSTRACT FROM AUTHOR]