Tilted Hardy paradoxes for device-independent randomness extraction

• URL: http://arxiv.org/abs/2205.02751v4
• Date: Tue, 12 Sep 2023 04:45:29 GMT
• Title: Tilted Hardy paradoxes for device-independent randomness extraction
• Authors: Shuai Zhao, Ravishankar Ramanathan, Yuan Liu, and Pawe{\l} Horodecki
• Abstract summary: We introduce a family of tilted Hardy paradoxes that allow to self-test general pure two-qubit entangled states. We also introduce a family of Hardy tests for maximally entangled states of local dimension $4, 8$ as the potential candidates for DI randomness extraction.
• Score: 5.802194744651422
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: The device-independent paradigm has had spectacular successes in randomness generation, key distribution and self-testing, however most of these results have been obtained under the assumption that parties hold trusted and private random seeds. In efforts to relax the assumption of measurement independence, Hardy's non-locality tests have been proposed as ideal candidates. In this paper, we introduce a family of tilted Hardy paradoxes that allow to self-test general pure two-qubit entangled states, as well as certify up to $1$ bit of local randomness. We then use these tilted Hardy tests to obtain an improvement in the generation rate in the state-of-the-art randomness amplification protocols for Santha-Vazirani (SV) sources with arbitrarily limited measurement independence. Our result shows that device-independent randomness amplification is possible for arbitrarily biased SV sources and from almost separable states. Finally, we introduce a family of Hardy tests for maximally entangled states of local dimension $4, 8$ as the potential candidates for DI randomness extraction to certify up to the maximum possible $2 \log d$ bits of global randomness.

Related papers

• Rényi divergence-based uniformity guarantees for $k$-universal hash functions [59.90381090395222]
  Universal hash functions map the output of a source to random strings over a finite alphabet. We show that it is possible to distill random bits that are nearly uniform, as measured by min-entropy.
  arXiv  Detail & Related papers  (2024-10-21T19:37:35Z)
• Controllable Generation via Locally Constrained Resampling [77.48624621592523]
  We propose a tractable probabilistic approach that performs Bayesian conditioning to draw samples subject to a constraint. Our approach considers the entire sequence, leading to a more globally optimal constrained generation than current greedy methods. We show that our approach is able to steer the model's outputs away from toxic generations, outperforming similar approaches to detoxification.
  arXiv  Detail & Related papers  (2024-10-17T00:49:53Z)
• Local contextuality-based self-tests are sufficient for randomness expansion secure against quantum adversaries [0.0]
  We show that local contextuality-based self-tests are sufficient to construct a randomness expansion protocol that is secure against unbounded quantum adversaries. Our protocol is based on self-testing from non-contextuality inequalities and we prove that our schemeally produces secure random numbers which are $mathcalO(mstepsilon)$-close to uniformly distributed and private.
  arXiv  Detail & Related papers  (2024-09-30T08:31:46Z)
• Doubly Robust Conditional Independence Testing with Generative Neural Networks [8.323172773256449]
  This article addresses the problem of testing the conditional independence of two generic random vectors $X$ and $Y$ given a third random vector $Z$. We propose a new non-parametric testing procedure that avoids explicitly estimating any conditional distributions.
  arXiv  Detail & Related papers  (2024-07-25T01:28:59Z)
• The Rate-Distortion-Perception Trade-off: The Role of Private Randomness [53.81648040452621]
  We show that private randomness is not useful if the compression rate is lower than the entropy of the source. We characterize the corresponding rate-distortion trade-off and show that private randomness is not useful if the compression rate is lower than the entropy of the source.
  arXiv  Detail & Related papers  (2024-04-01T13:36:01Z)
• Incorporating Zero-Probability Constraints to Device-Independent Randomness Expansion [11.765274200974774]
  We explore various forms of randomness that are certifiable in the so-called device-independent (DI) paradigm. In this work, we determine the certifiable randomness when zero-probability constraints are incorporated into the task of DI randomness expansion.
  arXiv  Detail & Related papers  (2024-01-16T15:57:17Z)
• Testing randomness of series generated in Bell's experiment [62.997667081978825]
  We use a toy fiber optic based setup to generate binary series, and evaluate their level of randomness according to Ville principle. Series are tested with a battery of standard statistical indicators, Hurst, Kolmogorov complexity, minimum entropy, Takensarity dimension of embedding, and Augmented Dickey Fuller and Kwiatkowski Phillips Schmidt Shin to check station exponent. The level of randomness of series obtained by applying Toeplitz extractor to rejected series is found to be indistinguishable from the level of non-rejected raw ones.
  arXiv  Detail & Related papers  (2022-08-31T17:39:29Z)
• Robust Learning of Optimal Auctions [84.13356290199603]
  We study the problem of learning revenue-optimal multi-bidder auctions from samples when the samples of bidders' valuations can be adversarially corrupted or drawn from distributions that are adversarially perturbed. We propose new algorithms that can learn a mechanism whose revenue is nearly optimal simultaneously for all true distributions'' that are $alpha$-close to the original distribution in Kolmogorov-Smirnov distance.
  arXiv  Detail & Related papers  (2021-07-13T17:37:21Z)
• The Sample Complexity of Robust Covariance Testing [56.98280399449707]
  We are given i.i.d. samples from a distribution of the form $Z = (1-epsilon) X + epsilon B$, where $X$ is a zero-mean and unknown covariance Gaussian $mathcalN(0, Sigma)$. In the absence of contamination, prior work gave a simple tester for this hypothesis testing task that uses $O(d)$ samples. We prove a sample complexity lower bound of $Omega(d2)$ for $epsilon$ an arbitrarily small constant and $gamma
  arXiv  Detail & Related papers  (2020-12-31T18:24:41Z)
• Revealing Incommensurability between Device-Independent Randomness, Nonlocality, and Entanglement using Hardy and Hardy-type Relations [0.0]
  We quantify randomness certified device-independently by using the Hardy and Cabello-Liang-Li (CLL) nonlocality relations. For the Hardy nonlocality, it is revealed that for a given amount of nonlocality signified by a particular non-zero value of the Hardy parameter, the amount of Hardy-certifiable randomness is not unique. On the other hand, for a given amount of CLL-nonlocality, the certifiable randomness is unique, similar to that for the CHSH nonlocality.
  arXiv  Detail & Related papers  (2020-11-25T05:10:54Z)
• Optimal rates for independence testing via $U$-statistic permutation tests [7.090165638014331]
  We study the problem of independence testing given independent and identically distributed pairs taking values in a $sigma$-finite, separable measure space. We first show that there is no valid test of independence that is uniformly consistent against alternatives of the form $f: D(f) geq rho2 $.
  arXiv  Detail & Related papers  (2020-01-15T19:04:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.