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arXiv:1611.01785 · Physical Review A

Leggett-Garg inequalities for squeezed states

Jérôme Martin, Vincent Vennin

Published Nov 28, 2016• 33 citations
arXivHTMLPDF

Abstract

Temporal Bell inequalities, or Leggett-Garg inequalities (LGIs), are studied for continuous-variable systems placed in a squeezed state. The importance of those systems lies in their broad applicability, which allows the description of many different physical settings in various branches of physics, ranging from cosmology to condensed matter physics and from optics to quantum information theory. Leggett-Garg inequality violations are explored and systematically mapped in squeezing parameter space. Configurations for which LGI violation occurs are found, but it is shown that no violation can be obtained if all squeezing angles vanish, contrary to what happens for the spatial Bell inequalities. We also assess the effect of decoherence on the detectability of such violations. Our study opens up the possibility of new experimental designs for the observation of LGI violation.

DOI
10.1103/physreva.94.052135

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Temporal Bell inequalities, or Leggett-Garg inequalities (LGIs), are studied for continuous-variable systems placed in a squeezed state. The importance of those systems lies in their broad applicability, which allows the description of many different physical settings in various branches of physics, ranging from cosmology to condensed matter physics and from optics to quantum information theory. Leggett-Garg inequality violations are explored and systematically mapped in squeezing parameter space. Configurations for which LGI violation occurs are found, but it is shown that no violation can be obtained if all squeezing angles vanish, contrary to what happens for the spatial Bell inequalities. We also assess the effect of decoherence on the detectability of such violations. Our study opens up the possibility of new experimental designs for the observation of LGI violation.
The Leggett-Garg inequality (LGI) is a temporal analogue of Bell's inequality and provides a quantitative test of the nonclassicality of a system through its violation. We analytically investigate the violation of the LGI in the context of photon-graviton conversion in a magnetic field background, motivated by its potential applications to testing the nonclassicality of gravity. When gravitational perturbations are quantized as gravitons, the conversion of an initial single photon state gives rise to a superposition of photon and graviton states. We show that the temporal correlations obtained from successive projective measurements on the photon-graviton system violate the LGI. Observation of such a violation would provide a novel avenue for probing the quantum nature of gravity.
Abstract Leggett–Garg inequality (LGI) is a time analogue of Bell’s inequality that concerns measurements performed on a system at different times. Violation to LGI indicates quantum coherence. We present a Leggett–Garg-type inequality compatible with more general neutrino oscillation frameworks, allowing the effects of decoherence to be taken into consideration. The inequality is applied to test coherence for data from Daya Bay, MINOS, and KamLAND experiments, and their results are compared to theoretical predictions to investigate decoherence. Both Daya Bay and MINOS data exhibit clear violations of over 10σ10\sigma 10σ 10σ , and of over 90 %\%% % of theoretical predictions, while the KamLAND data exhibit violation of 1.9σ1.9\sigma 1.9σ 1.9σ , being of 58 %\%% % of the theoretical prediction. The present work is the first to have considered the energy uncertainties in neutrino coherence tests.
In contrast to the spatial Bell's inequalities which probe entanglement between spatially separated systems, the Leggett–Garg inequalities test the correlations of a single system measured at different times. Violation of a genuine Leggett–Garg test implies either the absence of a realistic description of the system or the impossibility of measuring the system without disturbing it. Quantum mechanics violates the inequalities on both accounts and the original motivation for these inequalities was as a test for quantum coherence in macroscopic systems. The last few years has seen a number of experimental tests and violations of these inequalities in a variety of microscopic systems such as superconducting qubits, nuclear spins, and photons. In this article, we provide an introduction to the Leggett–Garg inequalities and review these latest experimental developments. We discuss important topics such as the significance of the non-invasive measurability assumption, the clumsiness loophole, and the role of weak measurements. Also covered are some recent theoretical proposals for the application of Leggett–Garg inequalities in quantum transport, quantum biology and nano-mechanical systems.
Macrorealism (MR) is the worldview that certain quantities may take definite values at all times irrespective of past or future measurements and may be experimentally falsified via the Leggett-Garg (LG) inequalities. We put this worldview to the test for systems described by a continuous variable xxx by seeking LG violations for measurements of a dichotomic variable Q=sign(x)Q=\text{sign}(x)Q=sign(x), in the case of Gaussian initial states in a quantum harmonic oscillator. Extending our earlier analysis [C. Mawby and J. J. Halliwell, Phys. Rev. A 105, 022221 (2022)], we find analytic expressions for the temporal correlators. An exploration of parameter space reveals significant regimes in which the two-time LG inequalities are violated, and likewise at three and four times. To obtain a physical picture of the LG violations, we exploit the continuous nature of the underlying position variable and analyze the relevant quantum-mechanical currents, Bohm trajectories, and Wigner function. We also show that larger violations are possible using the Wigner LG inequalities. Further, we extend the analysis to LG tests using coherent state projectors, thermal coherent states, and squeezed states.
The Leggett–Garg inequality (LGI), derived under the assumption of realism, acts as the temporal Bell inequality. It is studied in electromagnetic and strong interaction like photonics, superconducting qubits and nuclear spin. The weak interaction two-state oscillations of neutrinos affirmed the violation of Leggett–Garg-type inequalities (LGtI). We make an empirical test for the deviation of experimental results with the classical limits by analyzing the survival probability data of reactor neutrinos at a distinct range of baseline dividing energies, as an analog to a single neutrino detected at different times. A study of the updated data of the Daya Bay experiment unambiguously depicts an obvious cluster of data over the classical bound of LGtI and shows a 6.1σ6.1\sigma 6.1σ significance of the violation of them.