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arXiv:2512.11320 · Physical review. D/Physical review. D.

Concurrence fill and mode distribution of entanglement in neutrino oscillation

Rajrupa Banerjee, Prasanta Kumar Panigrahi, Hiranmaya Mishra, Sudhanwa Patra

Published Mar 5, 2026• 1 citation
arXivHTMLPDF

Abstract

The flavor oscillations in the neutrino system are known to be related to the multimode entanglement of a single particle state. Neutrino oscillations are shown to encompass not only quantum superposition among different mass eigenstates but also a single-particle multimode entanglement in the flavor basis as they propagate. In the framework of three flavor neutrino oscillations, 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 a three flavor neutrino system forms 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 bipartitioned entanglement measures, we derive the symmetric invariant and the concurrence fill, which quantify the distributed entanglement and are 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 General Long Baseline Experiment Simulator simulations within the DUNE setup 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 setup, the wide band of energy and expected higher sensitivity to C P violation at the second oscillation maximum provide a unique advantage to explore the quantum correlation effects across a broader energy window. Thus, the flavor coherence and C P -phase dependent interference can influence the quantum entanglement measures among neutrino flavor modes, and thereby, such potential new physics effects can be probed in current or future planned neutrino experiments.

DOI
10.1103/h72t-ndl2

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The flavor oscillations in the neutrino system are known to be related to the multimode entanglement of a single particle state. Neutrino oscillations are shown to encompass not only quantum superposition among different mass eigenstates but also a single-particle multimode entanglement in the flavor basis as they propagate. In the framework of three flavor neutrino oscillations, 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 a three flavor neutrino system forms 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 bipartitioned entanglement measures, we derive the symmetric invariant and the concurrence fill, which quantify the distributed entanglement and are 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 General Long Baseline Experiment Simulator simulations within the DUNE setup 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 setup, the wide band of energy and expected higher sensitivity to C P violation at the second oscillation maximum provide a unique advantage to explore the quantum correlation effects across a broader energy window. Thus, the flavor coherence and C P -phase dependent interference can influence the quantum entanglement measures among neutrino flavor modes, and thereby, such potential new physics effects can be probed in current or future planned neutrino experiments.
NNumerous neutrino experiments have confirmed the phenomenon of neutrino oscillation, providing direct evidence of the quantum mechanical nature of neutrinos. In this work, we investigate the entanglement properties of neutrino flavor states within the framework of three-flavor neutrino oscillation using two major entanglement measures: entanglement of formation (EOF) and concurrence, utilizing the DUNE experimental setup. Our findings indicate that the maximally entangled state appears between ν μ and ν τ whereas, ν e behaves as a nearly separable state. To further explore the nature of bipartite entanglement, we introduce the concept of the monogamy of entanglement, which allows us to investigate the distinction between genuine three-flavor entanglement and bipartite entanglement. Our analysis confirms that the three-flavor neutrino system forms a bipartite entanglement structure, adhering to the Coffman-Kundu-Wootters (CKW) inequality. Additionally, we implement a minimization procedure to find the best-fit values of the oscillation parameters that correspond to the concurrence minima at the two specific energy points where the concurrence reaches its lowest values. Using these best-fit values, we probe three fundamental unknowns in neutrino oscillation: CP violation sensitivity, neutrino mass hierarchy, and the octant issue of θ 23 , across two distinct energy points. Our results manifest that while the best-fit values obtained through concurrence minimization show slightly reduced sensitivity to CP violation compared to current best-fit values, they exhibit greater sensitivity to the mass hierarchy. Furthermore, the study reveals a maximal mixing angle for the atmospheric sector.
We investigate wave–particle–entanglement complementarity in three-flavor neutrino oscillations within a quantum information–theoretic framework. By considering three-flavor oscillation along with the possible entanglement between the detector and the propagation states, we extend beyond the usual wave-particle duality and arrive at a more complete triality description involving predictability, visibility, and entanglement. Using reduced density matrices and considering I-concurrence as an entanglement measure, we show that the total information carried by the system is conserved and naturally organized through the relation P 2 + V 2 + E 2 = 1 . While predictability and visibility exhibit the expected complementary behavior, we show that entanglement encodes additional wave-like information that is not captured by visibility alone. We apply our formalism to realistic long-baseline neutrino experiments, namely DUNE and T2K , and find that at the first oscillation maximum, a simultaneous characterization of the particle-like and wave-like nature of neutrinos becomes possible through the combined measurement of predictability and entanglement. Our results provide a unified operational interpretation of neutrino oscillations and highlight the role of quantum correlations in extending wave–particle duality to multipartite systems.
Abstract The violation of Leggett–Garg inequalities tested the quantumness of neutrino oscillations (NOs) across macroscopic distances. The quantumness can be quantified by using the tools of the quantum resource theories. Recently, a new genuine tripartite entanglement measure (Xie et al. in Phys Rev Lett 127:040403, 2021), concurrence fill, is defined as the square root of the area of the concurrence triangle satisfying all genuine multipartite entanglement conditions. It has several advantages compared to other existing tripartite measures. Here, we focus on using concurrence fill to quantify the tripartite entanglement in three-flavor NOs. Concurrence fill can reach its maximum 0.89 for the experimentally-observed electron antineutrino oscillations, but it cannot for the muon antineutrino oscillations. In both cases, we compare its performance with other three tripartite entanglement measures, including the generalized geometric measure (GGM), the three- π\pi π π entanglement, and the genuinely multipartite concurrence (GMC), in the neutrino propagation, and accordingly show that concurrence fill contains the most quantum resource. Furthermore, concurrence fill and the three- π\pi π π entanglement are always smooth, while GGM and GMC measures have several sharp peaks. The genuine tripartite quantification of the quantumness of three-flavor NOs represents the first step towards the further potential application of neutrinos on quantum information processing.
In the three-flavor neutrino oscillation framework, we investigate the transition probabilities of an initial muon neutrino flavor state in the presence of nonstandard interactions (NSIs) characterized by complex off-diagonal (∣εαβ∣eiφαβ|ε_{αβ}|e^{iφ_{αβ}}∣εαβ​∣eiφαβ​) and diagonal parameters (∣εαα−εββ∣|ε_{αα}-ε_{ββ}|∣εαα​−εββ​∣), including a CPCPCP-violating phase and a constant matter potential, under both normal (NO) and inverted mass ordering (IO) scenarios. Within these scenarios and through the lens of mode entanglement, bipartite entanglement measures such as entanglement entropy and capacity of entanglement are quantified in terms of the transition probabilities, which can be measured in neutrino oscillation experiments. Using these two bipartite entanglement measures, we further explore the quantum speed limit (QSL) time, which describes how rapidly bipartite entanglement evolves during neutrino oscillations. We illustrate our results using the baseline lengths and energies corresponding to ongoing long-baseline accelerator neutrino experiments, such as T2K, NOνννA, and the upcoming DUNE experiment. In the presence of a CPCPCP-violating phase and a constant matter potential, both with and without NSI effects, we compare the QSL time behavior for bipartite entanglement in neutrino oscillations for NO and IO. The most pronounced discrepancies in the QSL time for bipartite entanglement arise from the off-diagonal NSI parameter εμτε_{μτ}εμτ​ across both the NO and IO scenarios. We emphasize that among all the experiments considered, NOνννA and DUNE exhibit a rapid suppression of bipartite entanglement in neutrino oscillations in the standard oscillation scenario with NO at the end of their baseline lengths for the corresponding best-fit value of CPCPCP-violating phase. Our results hint at a possible imprint of new physics in neutrino oscillations.
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We present a quantum-information-theoretic study of three-flavor neutrino oscillations in long-baseline experiments by mapping flavor states to qubit-like representations and quantifying quantum correlations through total concurrence. The local minima of this entanglement measure identify energy regions where the flavor state is closest to separability, enabling cleaner extraction of oscillation parameters. We explain how these local minima offer opportunities for precision measurements and provide insight into the accurate determination of neutrino oscillation parameters. We then propose a strategy to improve parameter extraction by aligning the benchmark oscillation regions of NOνννA and T2K with the minimum entanglement achievable in each experiment. This shifts the concurrence minima toward higher-event-count energy regions, leading to tighter constraints and reducing the tension arising from their different energy regimes. For normal ordering, we obtain (0.581−0.0150+0.0136,195−32+38 ∘)(0.581^{+0.0136}_{-0.0150},195^{+38}_{-32}\,^\circ)(0.581−0.0150+0.0136​,195−32+38​∘) in the (sin⁡2θ23,δCP)(\sin^2θ_{23},δ_{\rm CP})(sin2θ23​,δCP​) plane and (0.580−0.0153+0.0140,2.515−0.0344+0.0344×10−3 eV2)(0.580^{+0.0140}_{-0.0153},2.515^{+0.0344}_{-0.0344}\times10^{-3}\,\mathrm{eV}^2)(0.580−0.0153+0.0140​,2.515−0.0344+0.0344​×10−3eV2) in the (sin⁡2θ23,Δm312)(\sin^2θ_{23},Δm^2_{31})(sin2θ23​,Δm312​) plane, yielding improved joint constraints. Using GLoBES simulations together with real data, we assess how local minima of quantum correlations influence leptonic CP-violation sensitivity, θ23θ_{23}θ23​ octant-degeneracy resolution, and mass-ordering determination. Our results show that minimizing entanglement can significantly affect these key sensitivities, highlighting quantum information measures as complementary probes of neutrino flavor oscillations and offering new insight into the role of quantum correlations in precision neutrino physics.