Neutrino oscillation is an important physical phenomenon in elementary particle physics, and its nonclassical features can be revealed by the Leggett-Garg inequality. It shows that its quantum coherence can be sustained over astrophysical length scales. In this work, we investigate the measure of quantumness in experimentally observed neutrino oscillations via the nonlocal advantage of quantum coherence (NAQC), quantum steering, and Bell nonlocality. From various neutrino sources, ensembles of reactor and accelerator neutrinos are analyzed at distinct energies, such as Daya Bay (0.5 km and 1.6 km) and MINOS (735 km) collaborations. The NAQC of two-flavor neutrino oscillation is characterized experimentally compared to the theoretical prediction. It exhibits non-monotonously evolutive phenomenon with the increase of energy. Furthermore, it is found that the NAQC is a stronger quantum correlation than quantum steering and Bell nonlocality even in the order of km. Hence, for an arbitrary bipartite neutrino-flavor state with achieving a NAQC, it must be also a steerable and Bell nonlocal state. The results might offer an insight into the neutrino oscillation for the further applications on quantum information processing.

Uncertainty relations take a crucial and fundamental part in the frame of quantum theory, and are bringing on many marvelous applications in the emerging field of quantum information sciences. Especially, as entropy is imposed into the uncertainty principle, entropy-based uncertainty relations lead to a number of applications including quantum key distribution, entanglement witness, quantum steering, quantum metrology, and quantum teleportation. Herein, the history of the development of the uncertainty relations is discussed, especially focusing on the recent progress with regard to quantum-memory-assisted entropic uncertainty relations and dynamical characteristics of the measured uncertainty in some explicit physical systems. The aims are to help deepen the understanding of entropic uncertainty relations and prompt further explorations for versatile applications of the relations on achieving practical quantum tasks.

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Neutrino oscillation is deemed as an interesting physical phenomenon and shows the nonclassical features made apparently by the Leggett–Garg inequality. The uncertainty principle is one of the fundamental features that distinguishes the quantum world to its classical counterpart. And the principle can be depicted in terms of entropy, which forms the so-called entropic uncertainty relations (EUR). In this work, the entropic uncertainty relations that are relevant to the neutrino-flavor states are investigated by comparing the experimental observation of neutrino oscillations to predictions. From two different neutrino sources, we analyze ensembles of reactor and accelerator neutrinos for different energies, including measurements performed by the Daya Bay collaboration using detectors at 0.5 and 1.6 km from their source, and by the MINOS collaboration using a detector with a 735km distance to the neutrino source. It is found that the entropy-based uncertainty conditions strengths exhibits non-monotonic evolutions as the energy increases. We also quantify the systemic quantumness measured by quantum correlation, and derive the intrinsic relationship between quantum correlation and EUR. Furthermore, we utilize EUR as a criterion to detect entanglement of neutrino-flavor state. Our results could illustrate the potential applications of neutrino oscillations on quantum information processing in the weak-interaction processes.

The uncertainty principle offers a bound to show accuracy of the simultaneous measurement outcome for two incompatible observables. In this letter, we investigate quantum-memoryassisted entropic uncertainty relation (QMA-EUR) when the particle to be measured stays at an open system, and another particle is treated as quantum memory under a noninertial frame. In such a scenario, the collective influence of the unital and nonunital noise environment, and of the relativistic motion of the system, on the QMA-EUR is examined. By numerical analysis, we conclude that, firstly, the noises and the Unruh effect can both increase the uncertainty, due to the decoherence of the bipartite system induced by the noise or Unruh effect; secondly, the uncertainty is more affected by the noises than by the Unruh effect from the acceleration; thirdly, unital noises can reduce the uncertainty in long-time regime. We give a possible physical interpretation for those results: that the information of interest is redistributed among the bipartite, the noisy environment and the physically inaccessible region in the noninertial frame. Therefore, we claim that our observations provide an insight into dynamics of the entropic uncertainty in a noninertial frame, and might be important to quantum precision measurement under relativistic motion.