Abstract Although neutrino–antineutrino states originating from neutral-current interactions are blind concerning the flavor state, an oscillation pattern is predicted provided that both neutrino and antineutrino are detected. This issue arises from both the coherence and entanglement of the neutrino–antineutrino states. Based on quantum resource theory, we use the $$l_1$$ l 1 -norm and concurrence to quantify quantum coherence and entanglement, respectively. Considering the localization properties by the wave packet approach and a matter potential which appears when neutrino and antineutrino propagate in a material medium, we obtain the $$l_1$$ l 1 -norm and concurrence. We see that the neutrino and antineutrino remain entangled for larger baseline lengths when they propagate in a material medium. In the case of the coherence property, the $$l_1$$ l 1 -norm decreases in comparison to the corresponding one in vacuum. However, its damping occurs for larger distances.
Abstract Although neutrino–antineutrino states originating from neutral-current interactions are blind concerning the flavor state, an oscillation pattern is predicted provided that both neutrino and antineutrino are detected. This issue arises from both the coherence and entanglement of the neutrino–antineutrino states. Based on quantum resource theory, we use the l1 l 1 -norm and concurrence to quantify quantum coherence and entanglement, respectively. Considering the localization properties by the wave packet approach and a matter potential which appears when neutrino and antineutrino propagate in a material medium, we obtain the l1 l 1 -norm and concurrence. We see that the neutrino and antineutrino remain entangled for larger baseline lengths when they propagate in a material medium. In the case of the coherence property, the l1 l 1 -norm decreases in comparison to the corresponding one in vacuum. However, its damping occurs for larger distances.
Abstract In this paper, we consider the quantum correlations, coherence and entanglement, in neutrino oscillation. We find that the l 1 -norm as a coherence measure is equal to the sum of the three possible concurrences for measuring the entanglement among different flavor modes which were calculated in the paper by Blasone M. et al ., EPL , 112 (2015) 20007. Our result shows that the origin of the flavor entanglement in neutrino oscillation is the same as that of quantum coherence. Furthermore, in the wave packet framework, the variation of the l 1 -norm is investigated by varying the wave packet width . As expected, the amount of coherence increases by due to the increase in overlapping of the mass eigenstates.
As the lynchpin of all quantum correlations, quantum coherence is fundamental for distinguishing quantum systems from classical ones and is essential for realizing quantum advantages in areas such as computation, communication, and metrology. In this study, we investigate the relationship between quantum coherence and neutrino oscillations within the two and three flavor-mode qubit frameworks. Our analysis extends beyond the commonly used l 1 -norm and relative entropy of coherence to include all relevant measures of coherence such as robustness of coherence, coherence concurrence, trace-norm distance measure of coherence, coherence of formation, Schatten- p -norm-based functionals, geometric coherence and logarithmic coherence rank, each offering unique insights into the quantum correlations in these systems. Notably, while the l 1 -norm and relative entropy-based measures apply to general quantum states, the other measures are particularly relevant for entangled systems, highlighting the critical role of entanglement in neutrino oscillations. We present a detailed methodology for calculating coherence measures in both two-flavor and three-flavor mixing scenarios, contributing to a deeper understanding of how quantum coherence manifests and evolves in mode-entangled neutrino systems. Our findings emphasize the potential of these systems as robust candidates for quantum information tasks, facilitated by the weak interaction nature of neutrinos.
Coherence, which represents the superposition of orthogonal states, is a fundamental concept in quantum mechanics and can also be precisely defined within quantum resource theory. Thus exploring quantum coherence in neutrino oscillations can not only help in examining the intrinsic quantum nature but can also explore their potential applications in quantum information technologies. Previous studies on quantum coherence have focused on neutrino flavor oscillations (FO). However, FO imply that neutrinos have mass, and this can lead to the generation of a tiny but finite magnetic dipole moment of neutrinos through quantum loop diagrams at higher orders of perturbative expansion of the interaction. This electromagnetic property of neutrinos can induce spin flavor oscillations (SFO) in the presence of an external magnetic field and hence is expected to enrich the study of coherence. In this work, we investigate quantum coherence in neutrino SFO with three flavor mixing within the interstellar as well as intergalactic magnetic fields, quantified by the l 1 norm and the relative entropy of coherence, and express these measures in terms of neutrino SFO probabilities. For FO, coherence measures can sustain higher values (say, within 50% of the maximum) over distances of several kilometers, which are relevant for terrestrial experiments like reactor and accelerator neutrinos. However, for SFO, we find that the coherence scale can extend to astrophysical distances, spanning from kiloparsecs to gigaparsecs.
If a neutrino or antineutrino produced in the decay of an unstable particle is not entangled to its accompanying particles, its mass is necessarily correlated with its momentum. In this manuscript, I illustrate that this entanglement would destroy the quantum coherence between the neutrino’s mass eigenstates in both the momentum and position representations, which was overlooked by other authors in previous investigations of entanglement and coherence associated with neutrino oscillations. I further point out that the states of a neutrino and an electron become nonseparable after their charged-current interaction. This nonseparability leads to decoherence for neutrinos propagating in matter, but was not taken into consideration in previous investigations of the matter effect.
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.
We evaluate the Hellinger-distance coherence of the two-flavor neutrino state subject to Lindblad damping of the mass-eigenstate interference term, and obtain a closed expression in terms of the flavor-basis density-matrix elements. In the two-flavor vacuum treatment with negligible wave-packet separation, the undamped state is pure, and the smallest eigenvalue of the damped state grows linearly with ε=1−κ, where κ=e−ΓL. An expansion about the pure state then yields a nonanalytic ε correction to the Hellinger coherence, with coefficient K=22usin2θ/1−2u, whereas the flavor-transition probability, the l1 coherence, the concurrence, the entanglement of formation and the local quantum Fisher information all respond linearly in ε. Using representative Daya Bay, KamLAND and MINOS working points together with a current 90% C.L. bound on energy-independent damping, we find fractional changes in the Hellinger coherence of 0.18%, 9.40% and 21.51%, against 0.0009%, 0.43% and 1.81% for the concurrence. The comparison concerns the response of the quantifiers to the damping parameter and carries no implication about experimental resolution. The same mechanism operates, with a different coefficient, for a correlated dephasing channel acting on the flavor coherence, where the non-Markovian regime produces damped revivals.