Bipartite Bell inequalities with three ternary-outcome measurements—from theory to experiments

Schwarz, Sacha; Bessire, Baenz; Stefanov, André; Liang, Yeong-Cherng

doi:10.1088/1367-2630/18/3/035001

Cited by 15 publications

(26 citation statements)

References 107 publications

(246 reference statements)

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“…Finding an expression I p¢ also requires methods of inference of the behavior of the device from a finite sample: indeed, the estimated behavior (18) cannot be used directly to find a candidate I p , as p almost always violates the no-signaling conditions. There exist different approaches to this inference (see for instance [20,[34][35][36][37]), so a nontrivial choice must be made.…”

Section: Bounding Randomness From Several Bell Expressions (T1)mentioning

confidence: 99%

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: Bounding Randomness From Several Bell Expressions (T1)mentioning

confidence: 99%

Device-independent randomness generation from several Bell estimators

et al. 2018

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“…[24] study a different variation of XOR games, so-called CHSH q games. [8] construct games based on random access codes, [34] investigate the advantages of using Chained Bell inequalities for randomness generation, and [31] explore Bell inequalities with ternary outcomes.…”

mentioning

confidence: 99%

Focus on device independent quantum information

2016

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The field of quantum information is born out of a sequence of surprising discoveries in the 1980s, all building on the same deep insight: the counter-intuitive quantum properties of particles such as photons or electrons can be put to task in order to accomplish certain computational, cryptographic, and information-theoretic tasks impossible to realize by purely classical means. A famous example is the cryptographic problem of key distribution, for which Bennett and Brassard devised the first quantum protocol in 1984 [6] and whose security relies on the no-cloning principle of quantum mechanics. Another example is the computational problem of factoring large numbers, for which Shor devised the first efficient quantum algorithm in 1994 [32] by exploiting the possibility for quantum systems to evolve in superpositions of exponentially many different states.In this early history, and until very recently, the violation of Bell inequalities was simply seen as yet another feature distinguishing the quantum processing of information from a classical one. It provided one of the initial motivations for developing a better understanding of entangled states; it was recognized as a key factor responsible for the quantum advantage in communication complexity protocols; it was frequently used in experiments to demonstrate oneʼs ability to generate and manipulate entanglement. It also played an important conceptual role, as it established that the predictions of quantum theory, including its claimed information processing advantages, could not be naively reproduced by a classical theory. But overall the manifestation of quantum non-locality was just another way to evidence the weirdness of quantum theory, on par with the nocloning principle or the uncertainty of quantum measurements in having little consequence for practical applications.In very recent years, however, the violation of Bell inequalities has acquired a special status that is starting to revolutionize our understanding of the information-theoretic possibilities of quantum information. Indeed, not only are the properties of quantum states and measurements leading to the violation of Bell inequalities unique in the sense of having no classical explanation, but they also often uniquely single out the quantum system itself. More precisely, given a black-box device that is verifiably violating a Bell inequality, quantum theory allows for a virtually unique way in which this can be accomplished. Furthermore, for the many tasks for which quantum information provides an advantage, there often turns out to be a protocol whose advantage essentially amounts to the sufficiently large violation of a certain Bell inequality.Taken together, these two phenomena lead to the following observation: it is possible to devise quantum information protocols whose correctness can be certified even when they are run with untrusted quantum devices, on which no a priori assumptions are made. Hence the name 'device-independence' (DI) to refer to such protocols. The implications of this are pr...

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“…When the considered resource is restricted to shared quantum correlations, inequality (26) and inequality (27) are instances of so-called device-independent witnesses for entanglement depth [26], i.e., Bell-like inequalities capable of certifying-directly from the observed correlation-a lower bound on the entanglement depth [59] of the measured system. More specifically, if the observed quantum value of the left-hand-side of Eq.…”

Section: Implications On Device-independent Certification Of Entanglementioning

confidence: 99%

Maximal violation of a broad class of Bell inequalities and its implication on self-testing

Jebarathinam

Hung

Chen

et al. 2019

Phys. Rev. Research

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In quantum information, lifting is a systematic procedure that can be used to derive-when provided with a seed Bell inequality-other Bell inequalities applicable in more complicated Bell scenarios. It is known that the procedure of lifting introduced by Pironio [J. Math. Phys. A 46, 062112 (2005)] preserves the facet-defining property of a Bell inequality. Lifted Bell inequalities therefore represent a broad class of Bell inequalities that can be found in all Bell scenarios. Here, we show that the maximal value of any lifted Bell inequality is preserved for both the set of nonsignaling correlations and quantum correlations. Despite the degeneracy in the maximizers of such inequalities, we show that the ability to self-test a quantum state is preserved under these lifting operations. In addition, except for outcome-lifting, local measurements that are self-testable using the original Bell inequality-despite the degeneracy-can also be self-tested using any lifted Bell inequality derived therefrom. While it is not possible to self-test all the positive-operator-valued measure elements using an outcome-lifted Bell inequality, we show that partial, but robust self-testing statements on the underlying measurements can nonetheless be made from the quantum violation of these lifted inequalities. We also highlight the implication of our observations on the usefulness of using lifted Bell-like inequalities as a device-independent witnesses for entanglement depth. The impact of the aforementioned degeneracy on the geometry of the quantum set of correlations is briefly discussed.

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Bipartite Bell inequalities with three ternary-outcome measurements—from theory to experiments

Abstract: In our article [1], we claimed to have given the first example of a facet-defining Bell inequality where a genuine positive-operator-valued (POVM) measure is relevant. Specifically, we claimed that any quantum realization of the maximal quantum violation of the Bell inequality I max 12

Cited by 15 publications

References 107 publications

Device-independent randomness generation from several Bell estimators

Device-independent randomness generation from several Bell estimators

Focus on device independent quantum information

Maximal violation of a broad class of Bell inequalities and its implication on self-testing

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