Concurrence fill and mode distribution of entanglement in neutrino oscillation

Abstract

In the framework of three flavor neutrino oscillation, we demonstrate that the measures of entanglement can be expressed in terms of experimentally accessible appearance and disappearance probabilities. We explicitly show here that the genuine tripartite entanglement measure, i.e., the tangle vanishes identically for all flavors signifying that three flavor neutrino system form a W-type entangled state. Further, we investigate alternative measures of tripartite entanglement like the partial tangle and the concurrence fill which capture the total sharing of entanglement beyond pairwise correlations. In terms of bipartite and bi-partitioned entanglement measures, we derive the symmetric invariant and the concurrence fill, which quantify the distributed entanglement completely expressible in terms of flavor transition probabilities. These entanglement measures display distinct energy dependent patterns across the oscillation window which can be experimentally accessible in the long baseline experiments like DUNE providing an alternative quantum information perspective on flavor evolution. We use GLobal Long Baseline Experiment Simulator (\textsf{GLoBES}) simulations within the DUNE set up to investigate these tripartite entanglement measures in terms of neutrino energy and the length of the baseline. It is observed that, at the point of maximal mixing, these measures show near maximal entanglement between the muon and the tau flavor modes establishing entanglement monogamy. Within the DUNE set up, the wide band of energy and expected higher sensitivity to CP-violation at second oscillation maximum provide a unique advantage to explore the quantum correlation effects across a broader energy window.