Infinite randomness expansion with a constant number of devices

Coudron, Matthew; Yuen, Henry

doi:10.1145/2591796.2591873

Cited by 56 publications

(64 citation statements)

References 27 publications

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“…In recent years several protocols for generating randomness in a DI way have been introduced [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], with varying degrees of security, rate of randomness expansion, or noise robustness. They all, however, share the feature that they rely on the estimation of a single Bell expression.…”

Section: Conclusion and Open Questionsmentioning

confidence: 99%

“…First, how to prove security against quantum side information when several Bell expressions or the full set of data generated in the experiment are taken into account? This is not a priori easy to answer since the analysis of most DIRNG protocols secure against quantum side information rely on Bell expressions with a particular structure [6,8,11] or, when they allow for arbitrary Bell expressions, do not optimally take into account the observed level of violation [17]. Second, we based the statistical analysis on the Azuma-Hoeffding inequality, but alternative deviation theorems [39] could be adapted to our setting.…”

Section: Conclusion and Open Questionsmentioning

confidence: 99%

“…This implies that bounds on the randomness as a function of f [p] have to be adapted to rely instead on the value of the Bell expression f estimated from experimental data. Some DIRNG and DIQKD protocols, and their security analyses, are reliant on specific Bell inequalities (usually the CHSH inequality) [6][7][8][9] or certain families of Bell inequalities [10][11][12], while others may be adapted to arbitrary Bell inequalities [3,[13][14][15][16][17]. However, to our knowledge all DIRNG and DIQKD protocols in the literature require that a single Bell inequality be chosen in advance and its experimental violation estimated (one exception is [18], where two fixed Bell expressions are used).…”

Section: Introductionmentioning

confidence: 99%

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Device-independent randomness generation from several Bell estimators

et al. 2018

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Device-independent randomness generation and quantum key distribution protocols rely on a fundamental relation between the non-locality of quantum theory and its random character. This relation is usually expressed in terms of a trade-off between the probability of guessing correctly the outcomes of measurements performed on quantum systems and the amount of violation of a given Bell inequality. However, a more accurate assessment of the randomness produced in Bell experiments can be obtained if the value of several Bell expressions is simultaneously taken into account, or if the full set of probabilities characterizing the behavior of the device is considered. We introduce protocols for device-independent randomness generation secure against classical side information, that rely on the estimation of an arbitrary number of Bell expressions or even directly on the experimental frequencies of measurement outcomes. Asymptotically, this results in an optimal generation of randomness from experimental data (as measured by the min-entropy), without having to assume beforehand that the devices violate a specific Bell inequality.

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Section: Conclusion and Open Questionsmentioning

confidence: 99%

Section: Conclusion and Open Questionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Device-independent randomness generation from several Bell estimators

et al. 2018

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“…Randomness is said to be expanded as an initial seed is converted into a larger amount of randomness [8]. The original scheme of Ref.[7] was able to achieve quadratic randomness expansion, while later, more sophisticated schemes, have now been shown to achieve better expansion, including exponential and unbounded expansion [10][11][12][13][14][15][16].Einstein-Podolsky-Rosen (EPR) steering [17] is a second form of quantum nonlocality, that considers the correlations between measurement outcomes of one party, and the states prepared (or 'steered') for a second party. From a modern perspective it is understood to constitute a one-sided-deviceindependent (1SDI) form of nonlocality, since it only relies on the characterisation of one set of measuring devices [18].…”

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confidence: 99%

Maximal Randomness Generation from Steering Inequality Violations Using Qudits

Skrzypczyk

Cavalcanti

2018

Phys. Rev. Lett.

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We consider the generation of randomness based upon the observed violation of an Einstein-Podolsky-Rosen (EPR) steering inequality, known as one-sided device-independent randomness generation. We show that in the simplest scenario-involving only two parties and two measurements for the uncharacterised party with d outcomes-that there exist EPR steering inequalities whose maximal violation certifies maximal randomness generation, equal to log(d) bits. We further show that all pure partially entangled full-Schmidt-rank states in all dimensions can achieve maximal violation of these inequalities, and thus lead to maximal randomness generation in the one-sided device-independent setting. More generally, the amount of randomness that can be generated is given by a semidefinite program, which we use to study the behavior for nonmaximal violations of the inequalities.

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“…[13], who showed how to amplify such source of randomness with the use of only eight noncommunicating devices. Their work was quickly followed by that of Coudron and Yuan [14], who showed how to use 20 non-communicating devices to obtain arbitrary many bits from a Santha-Vazirani source.…”

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confidence: 99%

Device-independent randomness extraction from an arbitrarily weak min-entropy source

et al. 2014

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Expansion and amplification of weak randomness plays a crucial role in many security protocols. Using quantum devices, such procedure is possible even without trusting the devices used, by utilizing correlations between outcomes of parts of the devices. We show here how to extract random bits with an arbitrarily low bias from a single arbitrarily weak min-entropy source in a device independent setting. To do this we use Mermin devices that exhibit super-classical correlations. Number of devices used scales polynomially in the length of the random sequence n. Our protocol is robust, it can tolerate devices that malfunction with a probability dropping polynomially in n at the cost of a minor increase of the number of devices used.High quality randomness is a very useful resource in many computation and cryptographic tasks. In fact it has been shown that many protocols (including quantum ones) vitally require perfect randomness for their security [1][2][3].Unfortunately, at the same time perfect randomness is very rare. In the classical world the true randomness, i.e. independent uniformly distributed random bits, cannot be produced at all. The only available resource is pseudo-randomness, sequences that appear random to all observers (often referred to as adversaries) not having full information about the whole environment. Thus classical randomness generators produce pseudorandom numbers stemming from external sources and fluctuations, hoping that the adversary will not be able to reconstruct all the background information. Sources producing imperfect randomness even taking into account the limited capabilities of the adversary are called weak random sources. To enhance the quality and security of these sources, randomness extractors are used. These are devices that combine more sources of randomness to obtain fewer bits of higher quality [4].On the other hand, theoretically the production of true randomness is possible, if one assumes Quantum theory to be valid: Preparation of a pure state and measurement in its complementary basis will yield a perfectly random result. This is due to the inherent randomness present in Quantum theory itself -this principle is being used in the design commercially available devices [5]. The assumption, however, is high quality and stability of quantum devices in an adversarial setting, which is far from trivial to achieve [6].In addition, quantum devices in reality act more like black boxes that are inaccessible for users except for providing them classical inputs and obtaining classical outputs from them. It is very hard, if not impossible, to directly test what these devices actually do, whether they perform operations and measurements as promised and whether their outputs really come from quantum measurements. Therefor it is crucial to test these devices even during their activity -satisfying these tests shall guarantee that the devices are correctly designed and manufactured and they work as desired. This is possible by utilizing super-classical correlations of certain quantum...

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Infinite randomness expansion with a constant number of devices

Cited by 56 publications

References 27 publications

Device-independent randomness generation from several Bell estimators

Device-independent randomness generation from several Bell estimators

Maximal Randomness Generation from Steering Inequality Violations Using Qudits

Device-independent randomness extraction from an arbitrarily weak min-entropy source

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