Robust self-testing of Bell inequalities tilted for maximal loophole-free nonlocality

• URL: http://arxiv.org/abs/2405.08743v1
• Date: Tue, 14 May 2024 16:31:06 GMT
• Title: Robust self-testing of Bell inequalities tilted for maximal loophole-free nonlocality
• Authors: Nicolas Gigena, Ekta Panwar, Giovanni Scala, Mateus Araújo, Máté Farkas, Anubhav Chaturvedi,
• Abstract summary: quantum strategies attain the maximal loophole-free nonlocality in the presence of inefficient detectors. We use a novel Jordan's lemma-based proof technique to obtain robust analytical self-testing statements for the entire family of tilted-Bell inequalities.
• Score: 1.099532646524593
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The degree of experimentally attainable nonlocality, as gauged by the amount of loophole-free violation of Bell inequalities, remains severely limited due to inefficient detectors. We address an experimentally motivated question: Which quantum strategies attain the maximal loophole-free nonlocality in the presence of inefficient detectors? For any Bell inequality and any specification of detection efficiencies, the optimal strategies are those that maximally violate a tilted version of the Bell inequality in ideal conditions. In the simplest scenario, we demonstrate that the quantum strategies that maximally violate the tilted versions of Clauser-Horne-Shimony-Holt inequality are unique up to local isometries. However, self-testing via the standard sum of squares decomposition method turns out to be analytically intractable since even high levels of the Navascu\'es--Pironio--Ac\'in hierarchy are insufficient to saturate the maximum quantum violation of these inequalities. Instead, we utilize a novel Jordan's lemma-based proof technique to obtain robust analytical self-testing statements for the entire family of tilted-Bell inequalities. These results allow us to unveil intriguing aspects of the effect of inefficient detectors and the complexity of characterizing the set of quantum correlations, in the simplest Bell scenario.

Related papers

• Device-independent randomness based on a tight upper bound of the maximal quantum value of chained inequality [11.658472781897123]
  We derive the tight upper bound of the maximum quantum value for chained Bell inequality with arbitrary number of measurements. Based on the tight upper bound we present the lower bounds on the device independent randomness with respect to the Werner states.
  arXiv  Detail & Related papers  (2023-05-23T14:10:03Z)
• PAPAL: A Provable PArticle-based Primal-Dual ALgorithm for Mixed Nash Equilibrium [58.26573117273626]
  We consider the non-AL equilibrium nonconptotic objective function in two-player zero-sum continuous games. Our novel insights into the particle-based algorithms for continuous distribution strategies are presented.
  arXiv  Detail & Related papers  (2023-03-02T05:08:15Z)
• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• Exponentially decreasing critical detection efficiency for any Bell inequality [0.34771439623170125]
  We propose a method for reducing the critical detection efficiency of any Bell inequality to arbitrary low values. The proposed method is based on the introduction of penalized $N$-product (PNP) Bell inequalities. The strength of our method is illustrated with a detailed study of the PNP Bell inequalities resulting from the Clauser-Horne-Shimony-Holt inequality.
  arXiv  Detail & Related papers  (2022-04-25T15:32:53Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• An elegant proof of self-testing for multipartite Bell inequalities [0.0]
  This work presents a simple and broadly applicable self-testing argument for N-partite correlation Bell inequalities with two binary outcome observables per party. To showcase the versatility of our proof technique, we obtain self-testing statements for N party Mermin-Ardehali-Bei-Klyshko (MABK) and Werner-Wolf-Weinfurter-.Zukowski-Brukner (WWW.ZB) family of linear Bell inequalities.
  arXiv  Detail & Related papers  (2022-02-14T18:00:50Z)
• Experimental violations of Leggett-Garg's inequalities on a quantum computer [77.34726150561087]
  We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
  arXiv  Detail & Related papers  (2021-09-06T14:35:15Z)
• Class of Bell-Clauser-Horne inequalities for testing quantum nonlocality [11.367526341820643]
  We propose methods for the rearrangement and linear inequality to prove a large variety of Bell-CH inequalities. We also derive a set of Bell-CH inequalities by using these methods which can be violated in some quantum entangled states.
  arXiv  Detail & Related papers  (2021-01-07T08:25:21Z)
• Violation of Bell inequalities by stochastic simulations of Gaussian States based on their positive Wigner representation [0.0]
  We study the use of an everywhere positive Wigner function as a probability density to perform simulations in quantum optics. Because of the difference between symmetrically and normally ordered operators, some trajectories in simulations can imply negative intensities, despite a positive mean. For the case of the Clauser-Horn Bell inequality, the influence of the quantum efficiency of the detectors is studied.
  arXiv  Detail & Related papers  (2020-06-28T08:12:27Z)
• Using Randomness to decide among Locality, Realism and Ergodicity [91.3755431537592]
  An experiment is proposed to find out, or at least to get an indication about, which one is false. The results of such experiment would be important not only to the foundations of Quantum Mechanics.
  arXiv  Detail & Related papers  (2020-01-06T19:26:32Z)
• Bell's theorem for trajectories [62.997667081978825]
  A trajectory is not an outcome of a quantum measurement, in the sense that there is no observable associated with it. We show how to overcome this problem by considering a special case of our generic inequality that can be experimentally tested point-by-point in time.
  arXiv  Detail & Related papers  (2020-01-03T01:40:44Z)

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.