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  $$10\sigma $$  <math> <mrow> <mn>10</mn> <mi>σ</mi> </mrow> </math>  , and of over 90 $$\%$$  <math> <mo>%</mo> </math>   of theoretical predictions, while the KamLAND data exhibit violation of  $$1.9\sigma $$  <math> <mrow> <mn>1.9</mn> <mi>σ</mi> </mrow> </math>  , being of 58 $$\%$$  <math> <mo>%</mo> </math>   of the theoretical prediction. The present work is the first to have considered the energy uncertainties in neutrino coherence tests.

China

Xing-Zhi Wang

Bo-Qiang Ma

New test of neutrino oscillation coherence with Leggett–Garg inequality

Inspired by Lefschetz thimble theory, we treat Quantum Field Theory as a statistical theory with a complex Probability Distribution Function (PDF). Such complex-valued PDFs permit the violation of Bell-type inequalities, which cannot be violated by a real-valued, non-negative PDF. In this paper, we consider the Classical-Statistical approximation in the context of Bell-type inequalities, viz. the familiar (spatial) Bell inequalities and the temporal Leggett-Garg inequalities. We show that the Classical-Statistical approximation does not violate temporal Bell-type inequalities, even though it is in some sense exact for a free theory, whereas the full quantum theory does. We explain the origin of this discrepancy, and point out the key difference between the spatial and temporal Bell-type inequalities. We comment on the import of this work for applications of the Classical-Statistical approximation.

United Kingdom

Peter Millington

Norway

United States

Zong-Gang Mou

Paul Saffin

Anders Tranberg

Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation

General Relativity enjoys the freedom of different geometrical interpretations in terms of curvature, torsion or non-metricity. Within this geometrical trinity, a simpler geometrical formulation of General Relativity manifests itself in the latter, where gravity is entirely attributed to non-metricity. In this Letter, we consider non-linear extensions of Coincident General Relativity <math><mi>f</mi><mo>(</mo><mover><mrow><mi>Q</mi></mrow><mrow><mo>˚</mo></mrow></mover><mo>)</mo></math> for phenomenological applications on both cosmological as well as galactic scales. The theory not only delivers dark energy on large scales but also recovers MOND on galactic scales, together with implications for the early universe cosmology. To the best of our knowledge, this represents the first relativistic, covariant, and ghost-free hybrid-formulation of MOND which recovers both, General Relativity and MOND in the appropriate limits and reconciles expected cosmological behavior. We further illustrate that previous bimetric formulations of MOND generically suffer from ghost instabilities and <math><mi>f</mi><mo>(</mo><mover><mrow><mi>Q</mi></mrow><mrow><mo>˚</mo></mrow></mover><mo>)</mo></math> crystalizes as a unique ghost-free theory.

Switzerland

Fabio D'Ambrosio

Mudit Garg

Lavinia Heisenberg

Non-linear extension of non-metricity scalar for MOND

The present work is devoted to the characterization of the Leggett-Garg inequality (LGI) for three flavored neutrino oscillations in the presence of both matter and charge-conjugation and parity violating effects. This study complements and completes the recent one put forward in arXiv:1710.05562 by relaxing the stationary condition. At variance with the latter case, the LGI contains interference terms which cannot be expressed in terms of experimentally measurable quantities, thus drawing a clear-cut distinction between the two scenarios, as well as highlighting the role of the stationary assumption on such systems. We find that the additional terms are small for a high energy neutrino beam compared to the maximum value attained by the Leggett-Garg parameter.

India

Javid Naikoo

Ashutosh Kumar Alok

Subhashish Banerjee

S. Uma Sankar

Leggett-Garg inequality in the context of three flavor neutrino oscillation

Entropic Leggett–Garg inequality is studied in systems like neutrinos in the context of two and three flavor neutrino oscillations and in neutral $$B_d$$ <math><msub><mi>B</mi><mi>d</mi></msub></math> , $$B_s$$ <math><msub><mi>B</mi><mi>s</mi></msub></math>  and K mesons. The neutrino dynamics is described with the matter effect taken into consideration. For the decohering B / K meson systems, the effect of decoherence and CP violation have also been taken into account, using the techniques of open quantum systems. Enhancement in the violation with increase in the number of measurements has been found, in consistency with findings in spin-s systems. The effect of decoherence is found to bring the deficit parameter $$\mathscr {D}^{[n]}$$ <math><msup><mi>D</mi><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow></msup></math>  closer to its classical value zero, as expected. The violation of entropic Leggett–Garg inequality lasts for a much longer time in K meson system than in $$B_d$$ <math><msub><mi>B</mi><mi>d</mi></msub></math>  and $$B_s$$ <math><msub><mi>B</mi><mi>s</mi></msub></math>  systems.

Entropic Leggett–Garg inequality in neutrinos and B(K) meson systems

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 6.1σ significance of the violation of them.

Qiang Fu

Xurong Chen

Testing violation of the Leggett–Garg-type inequality in neutrino oscillations of the Daya Bay experiment

Three-flavoured neutrino oscillations are investigated in the light of the Leggett–Garg inequality (LGI). The results obtained are: (a) The maximum violation of the LGI is 2.17036 for neutrino path length L1=140.15 km and ΔL=1255.7 km. (b) The presence of the mixing angle θ13 enhances the maximum violation of LGI by 4.6% . (c) The currently known mass hierarchy parameter α=0.0305 increases the maximum violation of LGI by 3.7% . (d) The presence of a CP-violating phase parameter enhances the maximum violation of LGI by 0.24% , thus providing an alternative indicator of CP violation in three-flavoured neutrino oscillations. The outline of an experimental proposal is suggested whereby the findings of this investigation may be verified.

Debashis Gangopadhyay

Animesh Sinha Roy

Three-flavoured neutrino oscillations and the Leggett–Garg inequality