Abstract
Since neutrino oscillations (NOs) show nonclassical features with the Leggett–Garg inequality and exhibit potential applications in quantum information processing and telecommunications, in order to further reveal quantum properties of the NO systems, we herein focus on investigating entanglement and entropic uncertainty relation in the context of three-flavor NOs. Specifically, we take advantage of three different types of entanglement measures to characterize quantum resources originating from NO systems, and examine the hierarchical relationship among them. Moreover, we analyze the experiment data from different neutrino sources including Daya Bay (0.5 and 1.6 km) and MINOS+ (735 km) collaborations in comparison with our theoretical results. We find that the dynamical evolution of both the entropic uncertainty and entanglement of system shows non-monotonicity, and the experimental results coincide with our theoretical prediction very well. Interestingly, it shows that neutrinos always maintain quantum properties during oscillation process. More importantly, we reveal that the variation of the uncertainty is almost anti-correlated with that of the entanglement of system. Therefore, the nature of entanglement and uncertainty in NOs can be explored in the practical experiment when the three-flavor neutrino states are treated as three-qubit ones, which might be useful for the potential NO-based applications on prospective quantum information processing.
Highlights
Degenerate mass eigenstates of the neutrino flavor states, the oscillation takes place in reality
As a matter of fact, MINOS+ is an updated version based on MINOS, the Main Injector Neutrino Oscillation Search (MINOS) experiment has been going on for seven years, from 2005 to 2012, and it can make accurate measurements of neutrino oscillation parameters over distance of 735 km by using the Neutrinos at the Main Injector (NuMI) neutrino beam and two detectors
We have observed the nonclassical features in neutrino oscillations through quantum entanglement and the measured uncertainty in the framework of initial electron and muon neutrinos
Summary
On the other hand, owing to the weak interactions of neutrinos, the decoherence effect during NOs is relatively weak compared with those in other particle systems that are widely utilized in the course of quantum-information processing. We treat the three neutrinos state as three-qubit system to explore their intrinsic quantum properties, and compare the corresponding theoretical predictions of the entropic uncertainty [32] and the entanglement [56–58] with those in experimental results from Daya Bay [3] and MINOS+ [6], respectively. This will benefit to quantification of the uncertainty and entanglement during realistic NOs, and represents a step towards the goal of practical quantum information processing via neutrino systems.
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