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

TL;DR

This paper explores a semi-device independent protocol for quantum random number expansion using n to 1 QRACs, demonstrating its effectiveness without requiring entanglement and identifying optimal parameters for maximum randomness.

Contribution

It introduces a new semi-device independent randomness expansion protocol based on n to 1 QRACs and analyzes its efficiency and optimal parameters.

Findings

Optimal n=3 for maximum randomness generation

Protocol does not require entanglement, simplifying implementation

Calculated min-entropy for the semi-device independent protocol

Abstract

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.