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

On constructions of quantum-secure device-independent randomness expansion protocols

Peter J. Brown

Published May 1, 2019• 2 citations
OpenAlex

Abstract

Device-independent randomness expansion protocols aim to expand a short uniformly random string into a much longer one whilst guaranteeing that their output is truly random. They are device-independent in the sense that this guarantee does not dependent on the specifics of an implementation. Rather, through the observation of nonlocal correlations we can conclude that the outputs generated are necessarily random. This thesis reports a general method for constructing these protocols and evaluating their security. Using this method, we then construct several explicit protocols and analyse their performance on noisy qubit systems. With a view towards near-future quantum technologies, we also investigate whether randomness expansion is possible using current nonlocality experiments. We find that, by combining the recent theoretical and experimental advances, it is indeed now possible to reliably and securely expand randomness.

Related papers

A Framework for Quantum-Secure Device-Independent Randomness Expansion

Peter J. Brown, Sammy Ragy, Roger Colbeck

A device-independent randomness expansion protocol aims to take an initial random seed and generate a longer one without relying on details of how the devices operate for security. A large amount of work to date has focussed on a particular protocol based on spot-checking devices using the CHSH inequality. Here we show how to derive randomness expansion rates for a wide range of protocols, with security against a quantum adversary. Our technique uses semidefinite programming and a recent improvement of the entropy accumulation theorem. To support the work and facilitate its use, we provide code that can generate lower bounds on the amount of randomness that can be output based on the measured quantities in the protocol. As an application, we give a protocol that robustly generates up to two bits of randomness per entangled qubit pair, which is twice that established in existing analyses of the spot-checking CHSH protocol in the low noise regime.

arXiv:1810.13346•IEEE Transactions on Information Theory•Dec 17, 2019•47 citations

A framework for quantum-secure device-independent randomness expansion

Peter J. Brown, Sammy Ragy, Roger Colbeck

A device-independent randomness expansion protocol aims to take an initial random seed and generate a longer one without relying on details of how the devices operate for security.A large amount of work to date has focussed on a particular protocol based on spot-checking devices using the CHSH inequality.Here we show how to derive randomness expansion rates for a wide range of protocols, with security against a quantum adversary.Our technique uses semidefinite programming and a recent improvement of the entropy accumulation theorem.To support the work and facilitate its use, we provide code that can generate lower bounds on the amount of randomness that can be output based on the measured quantities in the protocol.As an application, we give a protocol that robustly generates up to two bits of randomness per entangled qubit pair, which is twice that established in existing analyses of the spot-checking CHSH protocol in the low noise regime.

•May 1, 2020•13 citations

Improvements on Device Independent and Semi-Device Independent Protocols of Randomness Expansion

Rutvij Bhavsar

To generate genuine random numbers, random number generators based on quantum theory are essential. However, ensuring that the process used to produce randomness meets desired security standards can pose challenges for traditional quantum random number generators. This thesis delves into Device Independent (DI) and Semi-Device Independent (semi-DI) protocols of randomness expansion, based on a minimal set of experimentally verifiable security assumptions. The security in DI protocols relies on the violation of Bell inequalities, which certify the quantum behavior of devices. The semi-DI protocols discussed in this thesis require the characterization of only one device - a power meter. These protocols exploit the fact that quantum states can be prepared such that they cannot be distinguished with certainty, thereby creating a randomness resource. In this study, we introduce enhanced DI and semi-DI protocols that surpass existing ones in terms of output randomness rate, security, or in some instances, both. Our analysis employs the Entropy Accumulation Theorem (EAT) to determine the extractable randomness for finite rounds. A notable contribution is the introduction of randomness expansion protocols that recycle input randomness, significantly enhancing finite round randomness rates for DI protocols based on the CHSH inequality violation. In the final section of the thesis, we delve into Generalized Probability Theories (GPTs), with a focus on Boxworld, the largest GPT capable of producing correlations consistent with relativity. A tractable criterion for identifying a Boxworld channel is presented.

arXiv:2311.13528•Nov 22, 2023•0 citations

Device-independent information protocols: measuring dimensionality, randomness and nonlocality

Rodrigo Gallego López

The device-independent formalism is a set of tools to analyze experimental data and infer properties about systems, while avoiding almost any assumption about the functioning of devices. It has found applications both in fundamental and applied physics: some examples are the characterization of quantum nonlocality and information protocols for secure cryptography or randomness generation. This thesis contains novel results on these topics and also new applications such as deviceindependent test for dimensionality. After an introduction to the field, the thesis is divided in four parts. In the first we study device-independent tests for classical and quantum dimensionality. We investigate a scenario with a source and a measurement device. The goal is to infer, solely from the measurement statistics, the dimensionality required to describe the system. To this end, we exploit the concept of dimension witnesses. These are functions of the measurement statistics whose value allows one to bound the dimension. We study also the robustness of our tests in more realistic experimental situations, in which devices are affected by noise and losses. Lastly, we report on an experimental implementation of dimension witnesses. We conducted the experiment on photons manipulated in polarization and orbital angular momentum. This allowed us to generate ensembles of classical and quantum systems of dimension up to four. We then certified their dimension as well as its quantum nature by using dimension witnesses. The second part focuses on nonlocality. The local content is a nonlocality quantifier that represents the fraction of events that admit a local description. We focus on systems that exhibit, in that sense, maximal nonlocality. By exploiting the link between Kochen-Specker theorems and nonlocality, we derive a systematic recipe to construct maximally nonlocal correlations. We report on the experimental implementation of correlations with a high degree on nonlocality in comparison with all previous experiments on nonlocality. We also study maximally nonlocal correlations in the multipartite setting, and show that the so-called GHZ-state can be used to obtain correlations suitable for multipartite information protocols, such as secret-sharing. The third part studies nonlocality from an operational perspective. We study the set of operations that do not create nonlocality and characterize nonlocality as a resource theory. Our framework is consistent with the canonical definitions of nonlocality in the bipartite setting. However, we find that the well-established definition of multipartite nonlocality is inconsistent with the operational framework. We derive and analyze alternative definitions of multipartite nonlocality to recover consistency. Furthermore, the novel definitions of multipartite nonlocality allows us to analyze the validity of information principles to bound quantum correlations. We show that `information causality' and `non-trivial communication complexity' are insufficient to characterize the set of quantum correlations. In the fourth part we present the first quantum protocol attaining full randomness amplification. The protocol uses as input a source of imperfect random bits and produces full random bits by exploiting nonlocality. Randomness amplification is impossible in the classical regime and it was known to be possible with quantum system only if the initial source was almost fully random. Here, we prove that full randomness can indeed be certified using quantum non-locality under the minimal possible assumptions: the existence of a source of arbitrarily weak (but non-zero) randomness and the impossibility of instantaneous signaling. This implies that one is left with a strict dichotomic choice regarding randomness: either our world is fully deterministic or there exist events in nature that are fully random.

•Feb 22, 2013•3 citations

Experimental Realization of Device-Independent Quantum Randomness Expansion

Minghan Li, Xingjian Zhang, Wen‐Zhao Liu +12 more

Randomness expansion where one generates a longer sequence of random numbers from a short one is viable in quantum mechanics but not allowed classically. Device-independent quantum randomness expansion provides a randomness resource of the highest security level. Here, we report the first experimental realization of device-independent quantum randomness expansion secure against quantum side information established through quantum probability estimation. We generate $5.47\ifmmode\times\else\texttimes\fi{}{10}^{8}$ quantum-proof random bits while consuming $4.39\ifmmode\times\else\texttimes\fi{}{10}^{8}\text{ }\text{ }\mathrm{bits}$ of entropy, expanding our store of randomness by $1.08\ifmmode\times\else\texttimes\fi{}{10}^{8}\text{ }\text{ }\mathrm{bits}$ at a latency of about 13.1 h, with a total soundness error $4.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$. Device-independent quantum randomness expansion not only enriches our understanding of randomness but also sets a solid base to bring quantum-certifiable random bits into realistic applications.

arXiv:1902.07529•Physical Review Letters•Feb 4, 2021•69 citations

Local contextuality-based self-tests are sufficient for randomness expansion secure against quantum adversaries

Jaskaran Singh, Cameron Foreman, Kishor Bharti +1 more

In quantum cryptography, secure randomness expansion involves using a short private string of random bits to generate a longer one, even in the presence of an adversary who may have access to quantum resources. In this work, we demonstrate that local contextuality-based self-tests are sufficient to construct a randomness expansion protocol that is secure against computationally unbounded quantum adversaries. Our protocol is based on self-testing from non-contextuality inequalities and we prove that our scheme asymptotically produces secure random numbers which are $\mathcal{O}(m\sqrtε)$-close to uniformly distributed and private, where $ε$ is the robustness parameter of the self-test and $m$ is the length of the generated random bit string. Our protocol is semi-device-independent in the sense that it inherits any assumptions necessary for the underlying self-test.

arXiv:2409.20082•Sep 30, 2024•0 citations
Device-independent randomness expansion protocols aim to expand a short uniformly random string into a much longer one whilst guaranteeing that their output is truly random. They are device-independent in the sense that this guarantee does not dependent on the specifics of an implementation. Rather, through the observation of nonlocal correlations we can conclude that the outputs generated are necessarily random. This thesis reports a general method for constructing these protocols and evaluating their security. Using this method, we then construct several explicit protocols and analyse their performance on noisy qubit systems. With a view towards near-future quantum technologies, we also investigate whether randomness expansion is possible using current nonlocality experiments. We find that, by combining the recent theoretical and experimental advances, it is indeed now possible to reliably and securely expand randomness.
A device-independent randomness expansion protocol aims to take an initial random seed and generate a longer one without relying on details of how the devices operate for security. A large amount of work to date has focussed on a particular protocol based on spot-checking devices using the CHSH inequality. Here we show how to derive randomness expansion rates for a wide range of protocols, with security against a quantum adversary. Our technique uses semidefinite programming and a recent improvement of the entropy accumulation theorem. To support the work and facilitate its use, we provide code that can generate lower bounds on the amount of randomness that can be output based on the measured quantities in the protocol. As an application, we give a protocol that robustly generates up to two bits of randomness per entangled qubit pair, which is twice that established in existing analyses of the spot-checking CHSH protocol in the low noise regime.
A device-independent randomness expansion protocol aims to take an initial random seed and generate a longer one without relying on details of how the devices operate for security.A large amount of work to date has focussed on a particular protocol based on spot-checking devices using the CHSH inequality.Here we show how to derive randomness expansion rates for a wide range of protocols, with security against a quantum adversary.Our technique uses semidefinite programming and a recent improvement of the entropy accumulation theorem.To support the work and facilitate its use, we provide code that can generate lower bounds on the amount of randomness that can be output based on the measured quantities in the protocol.As an application, we give a protocol that robustly generates up to two bits of randomness per entangled qubit pair, which is twice that established in existing analyses of the spot-checking CHSH protocol in the low noise regime.
To generate genuine random numbers, random number generators based on quantum theory are essential. However, ensuring that the process used to produce randomness meets desired security standards can pose challenges for traditional quantum random number generators. This thesis delves into Device Independent (DI) and Semi-Device Independent (semi-DI) protocols of randomness expansion, based on a minimal set of experimentally verifiable security assumptions. The security in DI protocols relies on the violation of Bell inequalities, which certify the quantum behavior of devices. The semi-DI protocols discussed in this thesis require the characterization of only one device - a power meter. These protocols exploit the fact that quantum states can be prepared such that they cannot be distinguished with certainty, thereby creating a randomness resource. In this study, we introduce enhanced DI and semi-DI protocols that surpass existing ones in terms of output randomness rate, security, or in some instances, both. Our analysis employs the Entropy Accumulation Theorem (EAT) to determine the extractable randomness for finite rounds. A notable contribution is the introduction of randomness expansion protocols that recycle input randomness, significantly enhancing finite round randomness rates for DI protocols based on the CHSH inequality violation. In the final section of the thesis, we delve into Generalized Probability Theories (GPTs), with a focus on Boxworld, the largest GPT capable of producing correlations consistent with relativity. A tractable criterion for identifying a Boxworld channel is presented.
The device-independent formalism is a set of tools to analyze experimental data and infer properties about systems, while avoiding almost any assumption about the functioning of devices. It has found applications both in fundamental and applied physics: some examples are the characterization of quantum nonlocality and information protocols for secure cryptography or randomness generation. This thesis contains novel results on these topics and also new applications such as deviceindependent test for dimensionality. After an introduction to the field, the thesis is divided in four parts. In the first we study device-independent tests for classical and quantum dimensionality. We investigate a scenario with a source and a measurement device. The goal is to infer, solely from the measurement statistics, the dimensionality required to describe the system. To this end, we exploit the concept of dimension witnesses. These are functions of the measurement statistics whose value allows one to bound the dimension. We study also the robustness of our tests in more realistic experimental situations, in which devices are affected by noise and losses. Lastly, we report on an experimental implementation of dimension witnesses. We conducted the experiment on photons manipulated in polarization and orbital angular momentum. This allowed us to generate ensembles of classical and quantum systems of dimension up to four. We then certified their dimension as well as its quantum nature by using dimension witnesses. The second part focuses on nonlocality. The local content is a nonlocality quantifier that represents the fraction of events that admit a local description. We focus on systems that exhibit, in that sense, maximal nonlocality. By exploiting the link between Kochen-Specker theorems and nonlocality, we derive a systematic recipe to construct maximally nonlocal correlations. We report on the experimental implementation of correlations with a high degree on nonlocality in comparison with all previous experiments on nonlocality. We also study maximally nonlocal correlations in the multipartite setting, and show that the so-called GHZ-state can be used to obtain correlations suitable for multipartite information protocols, such as secret-sharing. The third part studies nonlocality from an operational perspective. We study the set of operations that do not create nonlocality and characterize nonlocality as a resource theory. Our framework is consistent with the canonical definitions of nonlocality in the bipartite setting. However, we find that the well-established definition of multipartite nonlocality is inconsistent with the operational framework. We derive and analyze alternative definitions of multipartite nonlocality to recover consistency. Furthermore, the novel definitions of multipartite nonlocality allows us to analyze the validity of information principles to bound quantum correlations. We show that `information causality' and `non-trivial communication complexity' are insufficient to characterize the set of quantum correlations. In the fourth part we present the first quantum protocol attaining full randomness amplification. The protocol uses as input a source of imperfect random bits and produces full random bits by exploiting nonlocality. Randomness amplification is impossible in the classical regime and it was known to be possible with quantum system only if the initial source was almost fully random. Here, we prove that full randomness can indeed be certified using quantum non-locality under the minimal possible assumptions: the existence of a source of arbitrarily weak (but non-zero) randomness and the impossibility of instantaneous signaling. This implies that one is left with a strict dichotomic choice regarding randomness: either our world is fully deterministic or there exist events in nature that are fully random.
Randomness expansion where one generates a longer sequence of random numbers from a short one is viable in quantum mechanics but not allowed classically. Device-independent quantum randomness expansion provides a randomness resource of the highest security level. Here, we report the first experimental realization of device-independent quantum randomness expansion secure against quantum side information established through quantum probability estimation. We generate $5.47\ifmmode\times\else\texttimes\fi{}{10}^{8}$ quantum-proof random bits while consuming $4.39\ifmmode\times\else\texttimes\fi{}{10}^{8}\text{ }\text{ }\mathrm{bits}$ of entropy, expanding our store of randomness by $1.08\ifmmode\times\else\texttimes\fi{}{10}^{8}\text{ }\text{ }\mathrm{bits}$ at a latency of about 13.1 h, with a total soundness error $4.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$. Device-independent quantum randomness expansion not only enriches our understanding of randomness but also sets a solid base to bring quantum-certifiable random bits into realistic applications.
In quantum cryptography, secure randomness expansion involves using a short private string of random bits to generate a longer one, even in the presence of an adversary who may have access to quantum resources. In this work, we demonstrate that local contextuality-based self-tests are sufficient to construct a randomness expansion protocol that is secure against computationally unbounded quantum adversaries. Our protocol is based on self-testing from non-contextuality inequalities and we prove that our scheme asymptotically produces secure random numbers which are O(mε)\mathcal{O}(m\sqrtε)O(mε​)-close to uniformly distributed and private, where εεε is the robustness parameter of the self-test and mmm is the length of the generated random bit string. Our protocol is semi-device-independent in the sense that it inherits any assumptions necessary for the underlying self-test.