Volume of violation of Bell-type inequalities as a measure of nonlocality

Barasiński, Artur; Nowotarski, Mateusz

doi:10.1103/physreva.98.022132

Cited by 17 publications

(13 citation statements)

References 45 publications

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“…From the higher chance of Bell inequality violation, we obtain a higher chance of achieving a non-zero key. This result also reverberates the results of the nonlocal volume 2 in [59][60][61][62][63][64], which increases for the pure bipartite entangled state when more measurement settings for each party are used. We observe the same phenomenon in our case, regarding the secret key rate.…”

Section: Random Measurement Settingssupporting

confidence: 68%

Device-independent secret key rates via a post-selected Bell inequality

Datta,

Kampermann,

Bruß

2021

Preprint

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We will relate and compare our method with theirs in the Results section (Sec. VI). In particular, we show that our procedure is advantageous in the nonasymptotic regime. This paper is organized as follows. We start in Sec. II by briefly reviewing classical and quantum correlations. Then we explain how to obtain the optimal Bell inequality from the observed probability distribution. We lay the framework to provide a confidence interval for the Bell expectation value in Sec. III. We provide an implementable DIQKD protocol in Sec. IV and calculate the finite-size secret key rate in Sec. V. In Sec. VI, we illustrate our method with several examples. II. GENERAL FRAMEWORKIn this section, we review the concept of the classical correlation polytope in Sec. II A and, based on this, we explain in Sec. II B how to construct Bell inequalities that are maximally violated by the measurement data. A. Set of correlationsConsider a set-up for two parties 1 (namely, Alice and Bob) connected by a quantum channel. The parties perform local measurements on a joint quantum state. Let us assume that Alice and Bob have m a and m b measurement settings, respectively. Alice's set of measurement settings is denoted as X = {1, • • • , m a }, and Bob's set of measurement settings as Y = {1, • • • , m b }. To estimate the probability distribution from the experimental data, we have to use the measurement device N times in succession. We assume that the devices behave independently and identically (i.i.d.) in each round, i.e. the results of the i th round are independent of the past 1 Note that our method can be extended in a straightforward way to n parties.

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Section: Random Measurement Settingssupporting

confidence: 68%

Device-independent secret key rates via a post-selected Bell inequality

Datta,

Kampermann,

Bruß

2021

Preprint

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“…The highest violation strength is observed for inequalities belonging to family (5) in 99.1% of random sets of settings, (6) in 0.85%, (7) in 0.04% and (8) in 0.01%. This means that in almost all cases we effectively use only two out of five settings.…”

Section: Statistical Relevance Of Facet Inequalitiesmentioning

confidence: 97%

“…The probability of violation of local realism under random measurements, proposed in [1], has gained considerable attention as an operational measure of nonclassicality of quantum states [2]. It has been demonstrated both numerically [3][4][5] and analytically [2,6] that this quantity is a good candidate for a nonlocality measure. What is more, in [6] it was proved that this quantifier satisfies some natural properties and expectations for an operational measure of nonclassicality.…”

Section: Introductionmentioning

confidence: 99%

Strength and typicality of nonlocality in multisetting and multipartite Bell scenarios

et al. 2020

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In this work we investigate the probability of violation of local realism under random measurements in parallel with the strength of these violations as described by resistance to white noise admixture. We address multisetting Bell scenarios involving up to 7 qubits. As a result, in the first part of this manuscript we report statistical distributions of a quantity reciprocal to the critical visibility for various multipartite quantum states subjected to random measurements. The statistical relevance of different classes of multipartite tight Bell inequalities violated with random measurements is investigated. We also introduce the concept of typicality of quantum correlations for pure states as the probability to generate a nonlocal behaviour with both random state and measurement. Although this typicality is slightly above 5.3% for the CHSH scenario, for a modest increase in the number of involved qubits it quickly surpasses 99.99%.

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“…and have a clear experimental interpretation. For instance, in an experimental setup based on correlated photons each correlation coefficient can be expressed as a function of coincidence counts measured on the detectors [16].…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…The probability of violation of local realism under random measurements, proposed in [12,13], has gained considerable attention as an operational measure of nonclassicality of quantum states [14]. It has been demonstrated both numerically [15][16][17][18] and analytically [14,19] that this quantity is a good candidate for a nonlocality measure. Furthermore, in [19] it was proved that this quantifier satisfies some natural properties and expectations for an operational measure of nonclassicality, e.g., invariance under local unitaries.…”

Section: Introductionmentioning

confidence: 99%

Experimentally friendly approach towards nonlocal correlations in multisetting N-partite Bell scenarios

Barasiński

Cernoch

Laskowski

et al. 2021

Quantum

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In this work, we study a recently proposed operational measure of nonlocality by Fonseca and Parisio [Phys. Rev. A 92, 030101(R) (2015)] which describes the probability of violation of local realism under randomly sampled observables, and the strength of such violation as described by resistance to white noise admixture. While our knowledge concerning these quantities is well established from a theoretical point of view, the experimental counterpart is a considerably harder task and very little has been done in this field. It is caused by the lack of complete knowledge about the facets of the local polytope required for the analysis. In this paper, we propose a simple procedure towards experimentally determining both quantities for N-qubit pure states, based on the incomplete set of tight Bell inequalities. We show that the imprecision arising from this approach is of similar magnitude as the potential measurement errors. We also show that even with both a randomly chosen N-qubit pure state and randomly chosen measurement bases, a violation of local realism can be detected experimentally almost 100% of the time. Among other applications, our work provides a feasible alternative for the witnessing of genuine multipartite entanglement without aligned reference frames.

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Volume of violation of Bell-type inequalities as a measure of nonlocality

Cited by 17 publications

References 45 publications

Device-independent secret key rates via a post-selected Bell inequality

Device-independent secret key rates via a post-selected Bell inequality

Strength and typicality of nonlocality in multisetting and multipartite Bell scenarios

Experimentally friendly approach towards nonlocal correlations in multisetting N-partite Bell scenarios

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