# Semi-Device-Independent Randomness Expansion Using n→1 Parity-Oblivious Quantum Random Access Codes

## TL;DR

This paper introduces a new method for generating secure randomness using quantum mechanics, which improves upon previous techniques by certifying more randomness under the same conditions.

## Contribution

The paper proposes a novel semi-device-independent randomness expansion protocol using n→1 parity-oblivious quantum random access codes.

## Key findings

- For n=4, the protocol achieves a higher success probability than previously reported.
- PO-QRAC-based protocols certify more randomness than standard QRAC-based protocols for the same quantum witness value.
- The 3→1 PO-QRAC protocol provides optimal randomness expansion under parity-obliviousness constraints.

## Abstract

Quantum mechanics enables the generation of genuine randomness through its intrinsic indeterminacy. In device-independent (DI) and semi-device-independent (SDI) frameworks, randomness generation protocols can further ensure that the output remains secure and unaffected by internal device imperfections, with certification grounded in violations of generalized Bell inequalities. In this work, we propose an SDI randomness expansion protocol using n→1 parity-oblivious quantum random access code (PO-QRAC), where the presence of true quantum randomness is certified through the violation of a two-dimensional quantum witness. For various values of n, we derive the corresponding maximal expected success probabilities. Notably, for n=4, the expected success probability obtained under our protocol exceeds the upper bound reported in prior work. Furthermore, we establish an analytic relationship between the certifiable min-entropy and the quantum witness value, and demonstrate that, for a fixed witness value, PO-QRAC–based protocols certify more randomness than those based on standard QRACs. Among all configurations satisfying the parity-obliviousness constraint, the protocol based on the 3→1 PO-QRAC achieves optimal randomness expansion performance.