Robust self-testing and certified randomness based on chained Bell inequality

• URL: http://arxiv.org/abs/2505.19917v1
• Date: Mon, 26 May 2025 12:40:57 GMT
• Title: Robust self-testing and certified randomness based on chained Bell inequality
• Authors: Rajdeep Paul, Sneha Munshi, Alok Kumar Pan,
• Abstract summary: The optimal quantum violation of a Bell inequality enables such a device-independent (DI) self-testing of the source and the measurement devices.<n>We devise an elegant sum-of-squares (SOS) technique enabling dimension-independent optimization of the quantum violation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Self-testing is the strongest certification procedure that uniquely characterizes the physical system based on the observed statistics, without any knowledge of the inner workings of the devices. The optimal quantum violation of a Bell inequality enables such a device-independent (DI) self-testing of the source and the measurement devices. In this work, we demonstrate the DI self-testing based on the chained Bell inequality. We devise an elegant sum-of-squares (SOS) technique enabling dimension-independent optimization of the quantum violation. Our approach enables the derivation of the state along with the relationship between the local observables directly from the optimization condition. This improves the previous methods of self-testing by deriving the state from the self-testing relation instead of assuming that the state is restricted to a two-qubit system. One significant aspect is the robustness of such self-testing in real experimental situations involving noise and imperfection, leading to deviation from the optimal quantum violation. We provide an analytical technique for robust self-testing in the presence of noise. As an application of our scheme, we demonstrate the generation of two bit DI randomness and analyze the robustness of such randomness.

Related papers

• Robust self-testing of the $m-$partite maximally entangled state and observables [0.0]
  We propose a simple and efficient self-testing protocol that certifies the state and observables based on the optimal quantum violation of the Svetlichny inequality. Our method leverages an elegant sum-of-squares approach to derive the optimal quantum value of the Svetlichny functional, devoid of assuming the dimension of the quantum system.
  arXiv  Detail & Related papers  (2024-08-20T11:03:37Z)
• Device-independent self-testing of unsharp measurements [0.0]
  Semi-device-independent certification of an unsharp instrument has recently been demonstrated. We provide device-independent (DI) self-testing of the unsharp instrument through the quantum violation of two Bell inequalities.
  arXiv  Detail & Related papers  (2023-11-08T06:34:47Z)
• Sequential Predictive Two-Sample and Independence Testing [114.4130718687858]
  We study the problems of sequential nonparametric two-sample and independence testing. We build upon the principle of (nonparametric) testing by betting.
  arXiv  Detail & Related papers  (2023-04-29T01:30:33Z)
• Near-Optimal Non-Parametric Sequential Tests and Confidence Sequences with Possibly Dependent Observations [44.71254888821376]
  We provide the first type-I-error and expected-rejection-time guarantees under general non-data generating processes. We show how to apply our results to inference on parameters defined by estimating equations, such as average treatment effects.
  arXiv  Detail & Related papers  (2022-12-29T18:37:08Z)
• Confidence-aware Training of Smoothed Classifiers for Certified Robustness [75.95332266383417]
  We use "accuracy under Gaussian noise" as an easy-to-compute proxy of adversarial robustness for an input. Our experiments show that the proposed method consistently exhibits improved certified robustness upon state-of-the-art training methods.
  arXiv  Detail & Related papers  (2022-12-18T03:57:12Z)
• Nonparametric Conditional Local Independence Testing [69.31200003384122]
  Conditional local independence is an independence relation among continuous time processes. No nonparametric test of conditional local independence has been available. We propose such a nonparametric test based on double machine learning.
  arXiv  Detail & Related papers  (2022-03-25T10:31:02Z)
• Self-Testing of a Single Quantum System: Theory and Experiment [5.9385501903680815]
  We develop a robust self-testing protocol based on the simplest contextuality witness for the simplest contextual quantum system. We apply the method in an experiment with randomly chosen measurements on a single trapped $40rm Ca+$ and near-perfect detection efficiency. We quantify and report that deviations from our assumptions are minimal, an aspect previously overlooked by contextuality experiments.
  arXiv  Detail & Related papers  (2022-03-17T00:48:30Z)
• Self-testing quantum states via nonmaximal violation in Hardy's test of nonlocality [0.0]
  A typical approach in designing such protocols is based on observing nonlocal correlations which exhibit maximum violation in a Bell test. We show that in Bell experiment known as Hardy's test of nonlocality not only the maximally nonlocal correlation self-tests a quantum state, rather a non-maximal nonlocal behavior can serve the same purpose.
  arXiv  Detail & Related papers  (2021-12-13T12:24:10Z)
• Sample-efficient device-independent quantum state verification and certification [68.8204255655161]
  Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing. We develop a systematic approach to device-independent verification of quantum states free of IID assumptions in the finite copy regime. We show that device-independent verification can be performed with optimal sample efficiency.
  arXiv  Detail & Related papers  (2021-05-12T17:48:04Z)
• Self-testing two-qubit maximally entangled states from generalized CHSH tests [0.0]
  We show how the self-testing of two-qubit maximally entangled states is improved by a refined analysis of measurement statistics. Our results not only provide novel insight into the set of quantum correlations suited for self-testing, but also facilitate the experimental implementations of device-independent certifications.
  arXiv  Detail & Related papers  (2020-11-05T19:00:00Z)
• Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits [58.720142291102135]
  We introduce a conditional witnessing technique to certify genuine multipartite entanglement (GME) We prove that the detection of entanglement in a linear number of bipartitions by a number of measurements scales linearly, suffices to certify GME. We apply our method to the noisy readout of stabilizer operators of the distance-three topological color code and its flag-based fault-tolerant version.
  arXiv  Detail & Related papers  (2020-10-06T18:00:07Z)
• Efficient Empowerment Estimation for Unsupervised Stabilization [75.32013242448151]
  empowerment principle enables unsupervised stabilization of dynamical systems at upright positions. We propose an alternative solution based on a trainable representation of a dynamical system as a Gaussian channel. We show that our method has a lower sample complexity, is more stable in training, possesses the essential properties of the empowerment function, and allows estimation of empowerment from images.
  arXiv  Detail & Related papers  (2020-07-14T21:10:16Z)

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.