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Quantum Information Processing

Semi-device-independent randomness expansion using $$n\rightarrow 1$$ sequential quantum random access codes

Xunan Wang, Jiabin Yuan, Yuqian Zhou, Ying Liu, Lili Fan

Published Oct 1, 2021• 3 citations
Publisher
DOI
10.1007/s11128-021-03234-6

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Semi-device-independent randomness expansion using n→1n\rightarrow 1n→1 sequential quantum random access codes
Semi-device-independent randomness certification with partially free random sources using 4→14\rightarrow 14→1 quantum random access code
Expanding the sharpness parameter area based on sequential 3→13{\rightarrow }13→1 parity-oblivious quantum random access code
We study random-number-expansion protocols based on the $n\ensuremath{\rightarrow}1$ 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 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 $n\ensuremath{\rightarrow}1$ QRACs with a view to their use in randomness-expansion protocols. We also calculate the dependence of the effectiveness of the randomness generation on nnn and find it optimal for n=3n=3n=3, and provide the explanation for this fact.
We have proved that new randomness can be certified by partially free sources using $2\ensuremath{\rightarrow}1$ quantum random access code (QRAC) in the framework of semi-device-independent (SDI) protocols [Y.-Q. Zhou, H.-W. Li, Y.-K. Wang, D.-D. Li, F. Gao, and Q.-Y. Wen, Phys. Rev. A 92, 022331 (2015)]. To improve the effectiveness of the randomness generation, here we propose the SDI randomness expansion using $3\ensuremath{\rightarrow}1$ QRAC and obtain the corresponding classical and quantum bounds of the two-dimensional quantum witness. Moreover, we get the condition which should be satisfied by the partially free sources to successfully certify new randomness, and the analytic relationship between the certified randomness and the two-dimensional quantum witness violation.