Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Effects of relaxed assumptions on semi-device-independent randomness expansion

Yukun Wang, Su‐Juan Qin, Tingting Song, Fen-Zhuo Guo, Wei Huang, Hui-Juan Zuo

Published Mar 11, 2014• 5 citations
Publisher

Abstract

Semi-device-independent randomness expansion is the protocol which can generate and certify perfect free random numbers, without making detailed assumptions on the internal working of quantum devices, except the bound on the dimension of the Hilbert space. The two-dimensional (2D) quantum witness violation has been used to generate guaranteed fresh randomness from untrusted devices in the prepare-and-measure configuration. In this paper we first show that the 2D quantum witness violation can be simulated by a classical deterministic process by relaxing the assumption of the dimension. A deterministic process to simulate the generation of random numbers is given, under the hidden variables model, with just the high dimensional measurement device and one qubit communication. This makes the generated number essentially deterministic, which is said to be pseudorandom. Then we also show that when we relax the freedom of choice, there is the exact region for which quantum correlations can be simulated by the classical process in the task of randomness expansion.

DOI
10.1103/physreva.89.032312

Related papers

Semi-device-independent random-number expansion without entanglement

Hong-Wei Li, Zhen−Qiang Yin, Yu-Chun Wu +5 more

By testing the classical correlation violation between two systems, true random numbers can be generated and certified without applying classical statistical method. In this work, we propose a true random-number expansion protocol without entanglement, where the randomness can be guaranteed only by the two-dimensional quantum witness violation. Furthermore, we only assume that the dimensionality of the system used in the protocol has a tight bound, and the whole protocol can be regarded as a semi-device-independent black-box scenario. Compared with the device-independent random-number expansion protocol based on entanglement, our protocol is much easier to implement and test.

arXiv:1108.1480•Physical Review A•Sep 14, 2011•128 citations

Security of Semi-Device-Independent Random Number Expansion Protocols

Dandan Li, Qiaoyan Wen, Yukun Wang +2 more

Semi-device-independent random number expansion (SDI-RNE) protocols require some truly random numbers to generate fresh ones, with making no assumptions on the internal working of quantum devices except for the dimension of the Hilbert space. The generated randomness is certified by non-classical correlation in the prepare-and-measure test. Until now, the analytical relations between the amount of the generated randomness and the degree of non-classical correlation, which are crucial for evaluating the security of SDI-RNE protocols, are not clear under both the ideal condition and the practical one. In the paper, first, we give the analytical relation between the above two factors under the ideal condition. As well, we derive the analytical relation under the practical conditions, where devices' behavior is not independent and identical in each round and there exists deviation in estimating the non-classical behavior of devices. Furthermore, we choose a different randomness extractor (i.e., two-universal random function) and give the security proof.

Scientific Reports•Oct 27, 2015•8 citations

Semi-device-independent randomness expansion with partially free random sources

Yuqian Zhou, Hongwei Li, Yukun Wang +3 more

By proposing device-independent protocols, Pironio et al. [Nature (London) 464, 1021 (2010)] and Colbeck et al. [Nat. Phys. 8, 450 (2012)] proved that new randomness can be generated by using perfectly free random sources or partially free ones as seed. Subsequently, Li et al. [Phys. Rev. A 84, 034301 (2011)] studied this topic in the framework of semi-device-independent and proved that new randomness can be obtained from perfectly free random sources. Here we discuss whether and how partially free random sources bring us new randomness in a semi-device-independent scenario. We propose a semi-device-independent randomness expansion protocol with partially free random sources and obtain the condition that the partially free random sources should satisfy to generate new randomness. In the process of analysis, we acquire a two-dimensional quantum witness. Furthermore, we get the analytic relationship between the generated randomness and the two-dimensional quantum witness violation.

arXiv:1503.03691•Physical Review A•Aug 13, 2015•16 citations

Source-Independent Quantum Random Number Generation with Partially Free Sources

Tong Wu, Yuqian Zhou, Qingle Wang +1 more

Random number generation is vital for cryptography. The classical world faces inherent limitations in generating provably true random numbers. Quantum mechanics, however, provides a natural foundation for genuinely unpredictable outcomes. In random number generation protocols, source-independent protocols ensure security even with untrusted source devices. Hence, we propose a sourceindependent expansion protocol with partially free sources to balance security and feasibility. In our proposed protocol, an untrusted source is interrogated by trusted measurement devices, utilizing a partially free source for randomness expansion. Based on Quantum random access codes (QRACs) in a three-dimensional Hilbert space with partially free source, we construct a quantum witness, derive the relationship between randomness generation efficiency and the violation of this witness. This demonstrates the advantage of utilizing higher-dimensional systems to generate more certified randomness.

International Symposium on AI and Cybersecurity (ISAICS)•Oct 24, 2025•0 citations

Semi-device-independent randomness expansion with partially free random sources using 3→1 quantum random access code

Yuqian Zhou, Fei Gao, Dandan Li +2 more

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.

Physical Review A•Sep 19, 2016•14 citations

Bounds on semi-device-independent quantum random-number expansion capabilities

Vaisakh Mannalath, Anirban Pathak

The randomness expansion capabilities of semi-device-independent (SDI) prepare and measure protocols are analyzed under the sole assumption that the Hilbert state dimension is known. It is explicitly proved that the maximum certifiable entropy that can be obtained through this set of protocols is $\ensuremath{-}{log}_{2}[\frac{1}{2}(1+\frac{1}{\sqrt{3}})]$ and the same is independent of the dimension witnesses used to certify the protocol. The minimum number of preparation and measurement settings required to achieve this entropy is also proven. An SDI protocol that generates the maximum output entropy with the least amount of input setting is provided. An analytical relationship between the entropy generated and the witness value is obtained. It is also established that certifiable entropy can be generated as soon as the dimension witness crosses the classical bound, making the protocol noise-robust and useful in practical applications.

arXiv:2111.14082•Physical Review A•Feb 23, 2022•8 citations
Semi-device-independent randomness expansion is the protocol which can generate and certify perfect free random numbers, without making detailed assumptions on the internal working of quantum devices, except the bound on the dimension of the Hilbert space. The two-dimensional (2D) quantum witness violation has been used to generate guaranteed fresh randomness from untrusted devices in the prepare-and-measure configuration. In this paper we first show that the 2D quantum witness violation can be simulated by a classical deterministic process by relaxing the assumption of the dimension. A deterministic process to simulate the generation of random numbers is given, under the hidden variables model, with just the high dimensional measurement device and one qubit communication. This makes the generated number essentially deterministic, which is said to be pseudorandom. Then we also show that when we relax the freedom of choice, there is the exact region for which quantum correlations can be simulated by the classical process in the task of randomness expansion.
By testing the classical correlation violation between two systems, true random numbers can be generated and certified without applying classical statistical method. In this work, we propose a true random-number expansion protocol without entanglement, where the randomness can be guaranteed only by the two-dimensional quantum witness violation. Furthermore, we only assume that the dimensionality of the system used in the protocol has a tight bound, and the whole protocol can be regarded as a semi-device-independent black-box scenario. Compared with the device-independent random-number expansion protocol based on entanglement, our protocol is much easier to implement and test.
Semi-device-independent random number expansion (SDI-RNE) protocols require some truly random numbers to generate fresh ones, with making no assumptions on the internal working of quantum devices except for the dimension of the Hilbert space. The generated randomness is certified by non-classical correlation in the prepare-and-measure test. Until now, the analytical relations between the amount of the generated randomness and the degree of non-classical correlation, which are crucial for evaluating the security of SDI-RNE protocols, are not clear under both the ideal condition and the practical one. In the paper, first, we give the analytical relation between the above two factors under the ideal condition. As well, we derive the analytical relation under the practical conditions, where devices' behavior is not independent and identical in each round and there exists deviation in estimating the non-classical behavior of devices. Furthermore, we choose a different randomness extractor (i.e., two-universal random function) and give the security proof.
By proposing device-independent protocols, Pironio et al. [Nature (London) 464, 1021 (2010)] and Colbeck et al. [Nat. Phys. 8, 450 (2012)] proved that new randomness can be generated by using perfectly free random sources or partially free ones as seed. Subsequently, Li et al. [Phys. Rev. A 84, 034301 (2011)] studied this topic in the framework of semi-device-independent and proved that new randomness can be obtained from perfectly free random sources. Here we discuss whether and how partially free random sources bring us new randomness in a semi-device-independent scenario. We propose a semi-device-independent randomness expansion protocol with partially free random sources and obtain the condition that the partially free random sources should satisfy to generate new randomness. In the process of analysis, we acquire a two-dimensional quantum witness. Furthermore, we get the analytic relationship between the generated randomness and the two-dimensional quantum witness violation.
Random number generation is vital for cryptography. The classical world faces inherent limitations in generating provably true random numbers. Quantum mechanics, however, provides a natural foundation for genuinely unpredictable outcomes. In random number generation protocols, source-independent protocols ensure security even with untrusted source devices. Hence, we propose a sourceindependent expansion protocol with partially free sources to balance security and feasibility. In our proposed protocol, an untrusted source is interrogated by trusted measurement devices, utilizing a partially free source for randomness expansion. Based on Quantum random access codes (QRACs) in a three-dimensional Hilbert space with partially free source, we construct a quantum witness, derive the relationship between randomness generation efficiency and the violation of this witness. This demonstrates the advantage of utilizing higher-dimensional systems to generate more certified randomness.
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.
The randomness expansion capabilities of semi-device-independent (SDI) prepare and measure protocols are analyzed under the sole assumption that the Hilbert state dimension is known. It is explicitly proved that the maximum certifiable entropy that can be obtained through this set of protocols is $\ensuremath{-}{log}_{2}[\frac{1}{2}(1+\frac{1}{\sqrt{3}})]$ and the same is independent of the dimension witnesses used to certify the protocol. The minimum number of preparation and measurement settings required to achieve this entropy is also proven. An SDI protocol that generates the maximum output entropy with the least amount of input setting is provided. An analytical relationship between the entropy generated and the witness value is obtained. It is also established that certifiable entropy can be generated as soon as the dimension witness crosses the classical bound, making the protocol noise-robust and useful in practical applications.