Exponentially decreasing critical detection efficiency for any Bell inequality

• URL: http://arxiv.org/abs/2204.11726v3
• Date: Thu, 1 Dec 2022 11:59:53 GMT
• Title: Exponentially decreasing critical detection efficiency for any Bell inequality
• Authors: Nikolai Miklin, Anubhav Chaturvedi, Mohamed Bourennane, Marcin Paw{\l}owski, Ad\'an Cabello
• Abstract summary: 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.
• Score: 0.34771439623170125
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We address the problem of closing the detection efficiency loophole in Bell experiments, which is crucial for real-world applications. Every Bell inequality has a critical detection efficiency $\eta$ that must be surpassed to avoid the detection loophole. Here, we propose a general method for reducing the critical detection efficiency of any Bell inequality to arbitrary low values. This is accomplished by entangling two particles in $N$ orthogonal subspaces (e.g., $N$ degrees of freedom) and conducting $N$ Bell tests in parallel. Furthermore, the proposed method is based on the introduction of penalized $N$-product (PNP) Bell inequalities, for which the so-called simultaneous measurement loophole is closed, and the maximum value for local hidden-variable theories is simply the $N$th power of the one of the Bell inequality initially considered. We show that, for the PNP Bell inequalities, the critical detection efficiency decays exponentially with $N$. The strength of our method is illustrated with a detailed study of the PNP Bell inequalities resulting from the Clauser-Horne-Shimony-Holt inequality.

Related papers

• An improved Bell-CHSH observable for gauge boson pairs [0.0]
  In this work, we consider Bell inequalities based on squares of spin operators. We find that our new choice of Bell operator has promising properties regarding states seen at colliders. We also conduct the first investigation of Bell violation in a system involving gauge bosons mediating different interactions.
  arXiv  Detail & Related papers  (2024-10-23T16:54:15Z)
• Optimizing Entanglement and Bell Inequality Violation in Top Anti-Top Events [5.151248813215795]
  We show that the basis which diagonalizes the spin-spin correlations is optimal for maximizing spin correlations, entanglement, and Bell inequality violation. We present the sensitivity for entanglement and Bell inequality violation in $tbar t$ events at the LHC and a future $e+e-$ collider.
  arXiv  Detail & Related papers  (2024-07-01T18:00:01Z)
• Robust self-testing of Bell inequalities tilted for maximal loophole-free nonlocality [1.099532646524593]
  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.
  arXiv  Detail & Related papers  (2024-05-14T16:31:06Z)
• Bell inequality is violated in $B^0\to J/\psi \, K^{\star}(892)^0$ decays [0.0]
  Entanglement is also present and the Bell inequality is violated in other decays of the $B$ mesons into vector mesons. We establish these distinguishing features of quantum mechanics at high energies in a collider setting.
  arXiv  Detail & Related papers  (2023-05-08T18:25:25Z)
• Why Should I Trust You, Bellman? The Bellman Error is a Poor Replacement for Value Error [83.10489974736404]
  We study the use of the Bellman equation as a surrogate objective for value prediction accuracy. We find that the Bellman error is a poor proxy for the accuracy of the value function.
  arXiv  Detail & Related papers  (2022-01-28T21:03:59Z)
• Optimal policy evaluation using kernel-based temporal difference methods [78.83926562536791]
  We use kernel Hilbert spaces for estimating the value function of an infinite-horizon discounted Markov reward process. We derive a non-asymptotic upper bound on the error with explicit dependence on the eigenvalues of the associated kernel operator. We prove minimax lower bounds over sub-classes of MRPs.
  arXiv  Detail & Related papers  (2021-09-24T14:48:20Z)
• Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priors [59.33977545294148]
  We show that $O(k log L)$ samples suffice to guarantee that the signal is close to any vector that minimizes an amplitude-based empirical loss function. We adapt this result to sparse phase retrieval, and show that $O(s log n)$ samples are sufficient for a similar guarantee when the underlying signal is $s$-sparse and $n$-dimensional.
  arXiv  Detail & Related papers  (2021-06-29T12:49:54Z)
• Learning Halfspaces with Tsybakov Noise [50.659479930171585]
  We study the learnability of halfspaces in the presence of Tsybakov noise. We give an algorithm that achieves misclassification error $epsilon$ with respect to the true halfspace.
  arXiv  Detail & Related papers  (2020-06-11T14:25:02Z)
• Bell nonlocality with a single shot [0.0]
  We show that to obtain a small expected p-value it is sufficient to have a large gap between the local and Tsirelson bounds of the Bell inequality. We present explicit examples of Bell inequalities with gap arbitrarily close to one, and show that this makes it possible to reject local hidden variables in a single shot.
  arXiv  Detail & Related papers  (2020-05-27T15:23:40Z)
• Non-Boolean Hidden Variables model reproduces Quantum Mechanics' predictions for Bell's experiment [91.3755431537592]
  Theory aimed to violate Bell's inequalities must start by giving up Boolean logic. "Hard" problem is to predict the time values when single particles are detected. "Soft" problem is to explain the violation of Bell's inequalities within (non-Boolean) Local Realism.
  arXiv  Detail & Related papers  (2020-05-20T21:46:35Z)
• Learning Near Optimal Policies with Low Inherent Bellman Error [115.16037976819331]
  We study the exploration problem with approximate linear action-value functions in episodic reinforcement learning. We show that exploration is possible using only emphbatch assumptions with an algorithm that achieves the optimal statistical rate for the setting we consider.
  arXiv  Detail & Related papers  (2020-02-29T02:02:40Z)

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.