Semi-Device-Independent Randomness Expansion Using <i>n</i>→1 Parity-Oblivious Quantum Random Access Codes

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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mspace width="-0.166667em"></mspace><mspace width="-0.166667em"></mspace><mo>→</mo><mspace width="-0.166667em"></mspace><mspace width="-0.166667em"></mspace><mn>1</mn></mrow></semantics></math></inline-formula> 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 <i>n</i>, we derive the corresponding maximal expected success probabilities. Notably, for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula>, 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mspace width="-0.166667em"></mspace><mspace width="-0.166667em"></mspace><mo>→</mo><mspace width="-0.166667em"></mspace><mspace width="-0.166667em"></mspace><mn>1</mn></mrow></semantics></math></inline-formula> PO-QRAC achieves optimal randomness expansion performance.