Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2307.04409 · Physical Review Letters

Violation of a Leggett-Garg Inequality Using Ideal Negative Measurements in Neutron Interferometry

Elisabeth Kreuzgruber, Richard Wagner, Niels Geerits, Hartmut Lemmel, Stephan Sponar

Published Jun 24, 2024• 11 citations
arXivHTMLPDF

Abstract

Leggett-Garg inequalities (LGIs) have been proposed in order to assess how far the predictions of quantum mechanics defy "macroscopic realism." With LGIs, correlations of measurements performed on a single system at different times are described. We report on an experiment that demonstrates the violation of an LGI with neutrons. The final measured value of the Leggett-Garg correlator K=1.120±0.007(stat)±0.019(sys), obtained in a neutron interferometric experiment, is clearly above the limit K=1 predicted by macrorealistic theories. The experimental results are analyzed within the framework of dynamical theory of neutron diffraction, evidently reproducing the obtained values.

DOI
10.1103/physrevlett.132.260201

Related papers

Violation of entropic Leggett-Garg inequality in nuclear spins

Hemant Katiyar, Abhishek Shukla, ‎K‎. ‎R‎. ‎K‎. ‎Rao +1 more

We report an experimental study of recently formulated entropic Leggett-Garg inequality (ELGI) by Usha Devi et al. [Phys. Rev. A 87, 052103 (2013)]. This inequality places a bound on the statistical measurement outcomes of dynamical observables describing a macrorealistic system. Such a bound is not necessarily obeyed by quantum systems, and therefore provides an important way to distinguish quantumness from classical behavior. Here we study ELGI using a two-qubit nuclear magnetic resonance system. To perform the noninvasive measurements required for the ELGI study, we prepare the system qubit in a maximally mixed state as well as use the ``ideal negative result measurement'' procedure with the help of an ancilla qubit. The experimental results show a clear violation of ELGI by over four standard deviations. These results agree with the predictions of quantum theory. The violation of ELGI is attributed to the fact that certain joint probabilities are not legitimate in the quantum scenario, in the sense they do not reproduce all the marginal probabilities. Using a three-qubit system, we also demonstrate that three-time joint probabilities do not reproduce certain two-time marginal probabilities.

arXiv:1210.1970•Physical Review A•May 2, 2013•68 citations

Experimental violation of the Leggett-Garg inequality in a three-level trapped-ion system

Tianxiang Zhan, Chun-Wang Wu, Manchao Zhang +9 more

Leggett-Garg inequality (LGI) is used to detect whether the macroscopic superposition state exists. Classical systems obey the LGI, but quantum systems may violate it. In the multilevel system, different state update rules determine different upper bounds of LGI. In this work, we experimentally test the LGI in a three-level trapped-ion system under the L\"uders and the von Neumann state update rules, respectively. The maximum observed value of the Leggett-Garg correlator under the von Neumann state update rule is ${K}_{3}=1.739\ifmmode\pm\else\textpm\fi{}0.014$, which demonstrates a violation of the L\"uders bound by 17 standard deviations and is by far the most significant violation under the specific model. The method used in our experiment could also be used in other multilevel experiments in the trapped-ion system.

arXiv:2209.07254•Physical Review A•Jan 25, 2023•9 citations

Quantum Nondemolition Measurement Enables Macroscopic Leggett-Garg Tests

Costantino Budroni, Giuseppe Vitagliano, Giorgio Colangelo +4 more

We show how a test of macroscopic realism based on Leggett-Garg inequalities (LGIs) can be performed in a macroscopic system. Using a continuous-variable approach, we consider quantum nondemolition (QND) measurements applied to atomic ensembles undergoing magnetically driven coherent oscillation. We identify measurement schemes requiring only Gaussian states as inputs and giving a significant LGI violation with realistic experimental parameters and imperfections. The predicted violation is shown to be due to true quantum effects rather than to a classical invasivity of the measurement. Using QND measurements to tighten the "clumsiness loophole" forces the stubborn macrorealist to recreate quantum backaction in his or her account of measurement.

arXiv:1503.08433•Physical Review Letters•Nov 12, 2015•44 citations

Experimental violation of the Leggett–Garg inequality in a three-level system

Hemant Katiyar, Aharon Brodutch, Dawei Lu +1 more

The Leggett–Garg (LG) test of macroscopic realism involves a series of dichotomic non-invasive measurements that are used to calculate a function which has a fixed upper bound for a macrorealistic system and a larger upper bound for a quantum system. The quantum upper bound depends on both the details of the measurement and the dimension of the system. Here we present an LG experiment on a three-level quantum system, which produces a larger theoretical quantum upper bound than that of a two-level quantum system. The experiment is carried out in nuclear magnetic resonance and consists of the LG test as well as a test of the ideal assumptions associated with the experiment, such as measurement non-invasiveness. The non-invasive measurements are performed via the modified ideal negative result measurement scheme on a three-level system. Once these assumptions are tested, the violation becomes small, despite the fact that the LG value itself is large. Our results showcase the advantages of using the modified measurement scheme that can reach higher LG values, since these leave a larger margin for violating the inequality in the face of experimental imperfections.

arXiv:1606.07151•New Journal of Physics•Jan 31, 2017•48 citations

Experimental violation of the Leggett-Garg inequality with a single-spin system

Maimaitiyiming Tusun, Wei Dong Cheng, Zihua Chai +4 more

Investigating the boundary between a quantum mechanical description and a classical realistic view is of fundamental importance. The Leggett-Garg (LG) inequality provides a criterion to distinguish between quantum systems and classical systems, and can be used to prove the macroscopic superposition state. A larger upper bound of the LG function can be obtained in a multilevel system. Here, we present an experimental violation of the Leggett-Garg inequality in a three-level system using a nitrogen-vacancy center in diamond by ideal negative result measurements. The experimental maximum value of the Leggett-Garg function is ${K}_{3}^{\text{expt}}=1.625\ifmmode\pm\else\textpm\fi{}0.022$, which exceeds the L\"uders bound with a $5\ensuremath{\sigma}$ level of confidence.

arXiv:2204.07765•Physical Review A•Apr 22, 2022•7 citations

Leggett-Garg inequalities and decays of unstable systems

Francesco Giacosa, Giuseppe Pagliara

We apply the Leggett-Garg inequalities (LGIs) to the cases of classical and quantum unstable systems. For classical systems the two assumptions of macroscopic realism and noninvasive measurements imply that the three-measurement string ${K}_{3}$ is identically equal to 1. Also, for quantum-mechanical systems, for which the two assumptions are, in general, not valid, we find that ${K}_{3}=1$ for purely exponential decays (${K}_{3}\ensuremath{\le}1$ is the general LGI). On the other hand, the necessary deviations from the exponential decay law at short and long times predicted by quantum mechanics lead to values of ${K}_{3}\ensuremath{\ne}1$. Moreover, a strict violation ${K}_{3}>1$ typically occurs at short times. Thus, we conclude that experiments in which such deviations from the exponential decay law have been observed should also have in their data violations of the LGIs.

arXiv:2104.04398•Physical Review A•Nov 29, 2021•4 citations
Leggett-Garg inequalities (LGIs) have been proposed in order to assess how far the predictions of quantum mechanics defy "macroscopic realism." With LGIs, correlations of measurements performed on a single system at different times are described. We report on an experiment that demonstrates the violation of an LGI with neutrons. The final measured value of the Leggett-Garg correlator K=1.120±0.007(stat)±0.019(sys), obtained in a neutron interferometric experiment, is clearly above the limit K=1 predicted by macrorealistic theories. The experimental results are analyzed within the framework of dynamical theory of neutron diffraction, evidently reproducing the obtained values.
We report an experimental study of recently formulated entropic Leggett-Garg inequality (ELGI) by Usha Devi et al. [Phys. Rev. A 87, 052103 (2013)]. This inequality places a bound on the statistical measurement outcomes of dynamical observables describing a macrorealistic system. Such a bound is not necessarily obeyed by quantum systems, and therefore provides an important way to distinguish quantumness from classical behavior. Here we study ELGI using a two-qubit nuclear magnetic resonance system. To perform the noninvasive measurements required for the ELGI study, we prepare the system qubit in a maximally mixed state as well as use the ``ideal negative result measurement'' procedure with the help of an ancilla qubit. The experimental results show a clear violation of ELGI by over four standard deviations. These results agree with the predictions of quantum theory. The violation of ELGI is attributed to the fact that certain joint probabilities are not legitimate in the quantum scenario, in the sense they do not reproduce all the marginal probabilities. Using a three-qubit system, we also demonstrate that three-time joint probabilities do not reproduce certain two-time marginal probabilities.
Leggett-Garg inequality (LGI) is used to detect whether the macroscopic superposition state exists. Classical systems obey the LGI, but quantum systems may violate it. In the multilevel system, different state update rules determine different upper bounds of LGI. In this work, we experimentally test the LGI in a three-level trapped-ion system under the L\"uders and the von Neumann state update rules, respectively. The maximum observed value of the Leggett-Garg correlator under the von Neumann state update rule is ${K}_{3}=1.739\ifmmode\pm\else\textpm\fi{}0.014$, which demonstrates a violation of the L\"uders bound by 17 standard deviations and is by far the most significant violation under the specific model. The method used in our experiment could also be used in other multilevel experiments in the trapped-ion system.
We show how a test of macroscopic realism based on Leggett-Garg inequalities (LGIs) can be performed in a macroscopic system. Using a continuous-variable approach, we consider quantum nondemolition (QND) measurements applied to atomic ensembles undergoing magnetically driven coherent oscillation. We identify measurement schemes requiring only Gaussian states as inputs and giving a significant LGI violation with realistic experimental parameters and imperfections. The predicted violation is shown to be due to true quantum effects rather than to a classical invasivity of the measurement. Using QND measurements to tighten the "clumsiness loophole" forces the stubborn macrorealist to recreate quantum backaction in his or her account of measurement.
The Leggett–Garg (LG) test of macroscopic realism involves a series of dichotomic non-invasive measurements that are used to calculate a function which has a fixed upper bound for a macrorealistic system and a larger upper bound for a quantum system. The quantum upper bound depends on both the details of the measurement and the dimension of the system. Here we present an LG experiment on a three-level quantum system, which produces a larger theoretical quantum upper bound than that of a two-level quantum system. The experiment is carried out in nuclear magnetic resonance and consists of the LG test as well as a test of the ideal assumptions associated with the experiment, such as measurement non-invasiveness. The non-invasive measurements are performed via the modified ideal negative result measurement scheme on a three-level system. Once these assumptions are tested, the violation becomes small, despite the fact that the LG value itself is large. Our results showcase the advantages of using the modified measurement scheme that can reach higher LG values, since these leave a larger margin for violating the inequality in the face of experimental imperfections.
Investigating the boundary between a quantum mechanical description and a classical realistic view is of fundamental importance. The Leggett-Garg (LG) inequality provides a criterion to distinguish between quantum systems and classical systems, and can be used to prove the macroscopic superposition state. A larger upper bound of the LG function can be obtained in a multilevel system. Here, we present an experimental violation of the Leggett-Garg inequality in a three-level system using a nitrogen-vacancy center in diamond by ideal negative result measurements. The experimental maximum value of the Leggett-Garg function is ${K}_{3}^{\text{expt}}=1.625\ifmmode\pm\else\textpm\fi{}0.022$, which exceeds the L\"uders bound with a $5\ensuremath{\sigma}$ level of confidence.
We apply the Leggett-Garg inequalities (LGIs) to the cases of classical and quantum unstable systems. For classical systems the two assumptions of macroscopic realism and noninvasive measurements imply that the three-measurement string K3{K}_{3}K3​ is identically equal to 1. Also, for quantum-mechanical systems, for which the two assumptions are, in general, not valid, we find that K3=1{K}_{3}=1K3​=1 for purely exponential decays (${K}_{3}\ensuremath{\le}1$ is the general LGI). On the other hand, the necessary deviations from the exponential decay law at short and long times predicted by quantum mechanics lead to values of ${K}_{3}\ensuremath{\ne}1$. Moreover, a strict violation K3>1{K}_{3}>1K3​>1 typically occurs at short times. Thus, we conclude that experiments in which such deviations from the exponential decay law have been observed should also have in their data violations of the LGIs.