Measurements of cosmic neutrinos have a reach potential for providing an insight into fundamental neutrino properties. For this a precise knowledge about an astrophysical environment of cosmic neutrinos propagation is needed. However this is not always possible, and the lack of information can bring about theoretical uncertainties in our physical interpretation of the results of experiments on cosmic neutrino fluxes. We formulate an approach that allows one to quantify the uncertainties using the apparatus of quantum measurement theory. We consider high-energy Dirac neutrinos emitted by some distant source and propagating towards Earth in the interstellar space. We take into account the neutrino magnetic moment interaction with stochastic interstellar magnetic fields and describe the neutrino evolution in the formalism of the Lindblad master equation for the neutrino density matrix. It is supposed that neutrinos on their way to Earth pass through highly magnetized dense layers of a cosmic object that ``stops'' left-handed neutrinos and lets only sterile, right-handed neutrinos to propagate farther. Such a filter mimics the strongest effect on the neutrino flux that can be induced by the cosmic object and that can be missed in the theoretical interpretation of the lab measurements due to the insufficient information about the astrophysical environment of the neutrino propagation. Treating the neutrino interaction with the neutrino filter of the cosmic object as the first, neutrino-spin measurement, whose result is not recorded, we study its invasive effect on the second, neutrino-flavor measurement in the lab. We quantify the invasiveness of the first, blind measurement by means of quantum witness that in the discussed case has an advantage over the well-known Leggett-Garg inequality, since the latter explores two-time correlation functions of the same operator. We solve analytically the Lindblad master equation for time evolution of the neutrino density matrix and on this basis we calculate the quantum witness for measuring cosmic electron neutrinos in the lab. We present numerical illustrations of the robust invasive effect showing that the quantum witness as a function of the distance between Earth and a cosmic object can be an asymptotically nonvanishing quantity despite the thermalization of the neutrino spin induced by stochastic interstellar magnetic fields.
Measurements of cosmic neutrinos have a reach potential for providing an insight into fundamental neutrino properties. For this a precise knowledge about an astrophysical environment of cosmic neutrinos propagation is needed. However this is not always possible, and the lack of information can bring about theoretical uncertainties in our physical interpretation of the results of experiments on cosmic neutrino fluxes. We formulate an approach that allows one to quantify the uncertainties using the apparatus of quantum measurement theory. We consider high-energy Dirac neutrinos emitted by some distant source and propagating towards Earth in the interstellar space. We take into account the neutrino magnetic moment interaction with stochastic interstellar magnetic fields and describe the neutrino evolution in the formalism of the Lindblad master equation for the neutrino density matrix. It is supposed that neutrinos on their way to Earth pass through highly magnetized dense layers of a cosmic object that ``stops'' left-handed neutrinos and lets only sterile, right-handed neutrinos to propagate farther. Such a filter mimics the strongest effect on the neutrino flux that can be induced by the cosmic object and that can be missed in the theoretical interpretation of the lab measurements due to the insufficient information about the astrophysical environment of the neutrino propagation. Treating the neutrino interaction with the neutrino filter of the cosmic object as the first, neutrino-spin measurement, whose result is not recorded, we study its invasive effect on the second, neutrino-flavor measurement in the lab. We quantify the invasiveness of the first, blind measurement by means of quantum witness that in the discussed case has an advantage over the well-known Leggett-Garg inequality, since the latter explores two-time correlation functions of the same operator. We solve analytically the Lindblad master equation for time evolution of the neutrino density matrix and on this basis we calculate the quantum witness for measuring cosmic electron neutrinos in the lab. We present numerical illustrations of the robust invasive effect showing that the quantum witness as a function of the distance between Earth and a cosmic object can be an asymptotically nonvanishing quantity despite the thermalization of the neutrino spin induced by stochastic interstellar magnetic fields.
Abstract There are two types of uncertainties related to the measurements done on a quantum system: statistical and those related to non-commuting observables and incompatible measurements. The latter indicates the quantum system’s inherent nature and is in the scope of the present study. We explore uncertainties related to the interstellar ultrahigh-energy neutrino and introduce a novel concept: quantum spin-flavour memory. Advanced uncertainty measures are entropic measures, and the effect of the quantum memory reduces the uncertainty. The problem in question corresponds to a real physical event: high-energy Dirac neutrinos emitted by some distant source and propagating towards the earth. The neutrino has a finite magnetic moment and interacts with both deterministic and stochastic interstellar magnetic fields. To describe the effect of a noisy environment, we exploit the Lindblad master equation for the neutrino density matrix. Quantum spin-flavour memory is quantified in terms of the generalized Kraus’s trade-off relation. This trade-off relation converts to the equality when quantum memory is absent. We discovered that while most measures of quantum correlations show their irrelevance, the quantum spin-flavour discord is the quantifier of the quantum spin-flavour memory.
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.
Neutrino oscillation represents an intriguing physical phenomenon where the quantumness can be maintained and detected over a long distance. Previously, the nonclassical character of neutrino oscillation was tested with the Leggett-Garg inequality, where a clear violation of the classical bound was observed [J. A. Formaggio et al., Phys. Rev. Lett. 117, 050402 (2016)]. However, there are several limitations in testing neutrino oscillations with the Leggett-Garg inequality. In particular, the degree of violation of the Leggett-Garg inequality cannot be taken as a ``measure of quantumness.'' Here, we focus on quantifying the quantumness of experimentally observed neutrino oscillation, using the tools of the recently developed quantum resource theory. We analyzed ensembles of reactor and accelerator neutrinos at distinct energies from a variety of neutrino sources, including Daya Bay (0.5 and 1.6 km), KamLAND (180 km), MINOS (735 km), and T2K (295 km). The quantumness of the three-flavored neutrino oscillation is characterized within a $3\ensuremath{\sigma}$ range relative to the theoretical prediction. It is found that the maximal coherence was observed in the neutrino source from the KamLAND reactor. However, even though the survival probability of the Daya Bay experiment did not vary significantly (it dropped about 10%), the coherence recorded can reach up to 40% of the maximal value. These results represent the longest distance over which quantumness was experimentally determined for quantum particles other than photons.
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.
We present a general open-quantum-system framework to model decoherence induced by stochastic Planck-scale fluctuations of spacetime, focusing on the κ -Minkowski noncommutative geometry as a representative quantum gravity scenario. Treating the deformation parameter as Gaussian white noise, we derive a Lindblad-type master equation applicable to arbitrary quantum systems and obtain a distinctive inverse-energy scaling of the decoherence rate, Γ ∝ E − 4 . As an illustrative example, we analyze a three-level system motivated by neutrino flavor oscillations and derive closed-form expressions for survival and transition probabilities with spacetime-induced damping. The E − 4 scaling contrasts sharply with the positive power laws often invoked in quantum gravity phenomenology and predicts negligible decoherence for high-energy neutrinos—consistent with IceCube observations—while implying that the strongest effects arise in the extreme low-energy regime. In this context, the sub-eV-scale energies characteristic of the cosmic neutrino background provide a natural infrared benchmark for illustrating the enhanced sensitivity to quantum spacetime fluctuations. Our results establish a unified formalism connecting quantum information methods, open-system dynamics, and quantum spacetime phenomenology, thereby offering a framework for exploring potential signatures of Planck-scale physics in future low-energy neutrino studies.
We present a general open-quantum-systems framework to model decoherence induced by stochastic Planck-scale fluctuations of spacetime, focusing on the kappa-Minkowski noncommutative geometry as a representative quantum-gravity scenario. Treating the deformation parameter as Gaussian white noise, we derive a Lindblad-type master equation applicable to arbitrary quantum systems and obtain a distinctive inverse-energy scaling of the decoherence rate, Gamma proportional to E^{-4}. As an illustrative example, we analyze a three-level system motivated by neutrino flavor oscillations and derive closed-form expressions for survival and transition probabilities with spacetime-induced damping. The E^{-4} scaling contrasts sharply with the positive power laws often invoked in quantum-gravity phenomenology and predicts negligible decoherence for high-energy neutrinos consistent with IceCube observations, while implying that the strongest effects arise in the extreme low-energy regime. In this context, the sub-eV-scale energies characteristic of the cosmic neutrino background provide a natural infrared benchmark for illustrating the enhanced sensitivity to quantum-spacetime fluctuations. Our results establish a unified formalism connecting quantum-information methods, open-system dynamics, and quantum-spacetime phenomenology, thereby offering a framework for exploring potential signatures of Planck-scale physics in future low-energy neutrino studies.