Semi-device independent random number expansion protocol with n to 1 quantum random access codes

We study random number expansion protocols based on the $n \to 1$ quantum random access codes (QRACs). We consider them in the semi-device independent scenario where the inner workings of the devices are unknown to us but we can certify the dimensions of the systems being communicated. This approach does not require the use of the entanglement and makes the physical realization of these protocols much easier than in the standard device independent scenario. In our work, we propose a protocol for randomness expansion, compute min-entropy for the semi-device independent protocol, and investigate $n\to 1$ QRACs with a view to their use in randomness expansion protocols. We also calculate the dependence of the effectiveness of the randomness generation on $n$ and find it optimal for $n=3$, and provide the explanation for this fact.