The quantum speed limits (QSLs) set fundamental lower bounds on the time required for a quantum system to evolve from a given initial state to a final state. In this work, we investigate C P violation and the mass ordering problem of neutrino oscillations in matter using the QSL time as a key analytical tool. We examine the QSL time for the unitary evolution of two- and three-flavor neutrino states, both in vacuum and in the presence of matter. Two-flavor neutrino oscillations are used as a precursor to their three-flavor counterparts. We further compute the QSL time for neutrino state evolution and entanglement in terms of neutrino survival and oscillation probabilities, which are experimentally measurable quantities in neutrino experiments. A difference in the QSL time between the normal and inverted mass ordering scenarios, for neutrino state evolution as well as for entanglement, under the effect of a C P violation phase is observed. Our results are illustrated using the length scales and energies of ongoing long-baseline accelerator neutrino experiments such as T2K, NOvA, and the upcoming DUNE experiment. Notably, three-flavor neutrino oscillations in constant matter density exhibit faster state evolution across all these neutrino experiments in the normal mass ordering scenario. Additionally, we observe fast entanglement suppression in DUNE assuming a normal mass ordering.
The quantum speed limits (QSLs) set fundamental lower bounds on the time required for a quantum system to evolve from a given initial state to a final state. In this work, we investigate C P violation and the mass ordering problem of neutrino oscillations in matter using the QSL time as a key analytical tool. We examine the QSL time for the unitary evolution of two- and three-flavor neutrino states, both in vacuum and in the presence of matter. Two-flavor neutrino oscillations are used as a precursor to their three-flavor counterparts. We further compute the QSL time for neutrino state evolution and entanglement in terms of neutrino survival and oscillation probabilities, which are experimentally measurable quantities in neutrino experiments. A difference in the QSL time between the normal and inverted mass ordering scenarios, for neutrino state evolution as well as for entanglement, under the effect of a C P violation phase is observed. Our results are illustrated using the length scales and energies of ongoing long-baseline accelerator neutrino experiments such as T2K, NOvA, and the upcoming DUNE experiment. Notably, three-flavor neutrino oscillations in constant matter density exhibit faster state evolution across all these neutrino experiments in the normal mass ordering scenario. Additionally, we observe fast entanglement suppression in DUNE assuming a normal mass ordering.
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) and diagonal parameters (∣εαα−εββ∣), including a CP-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, NOνA, and the upcoming DUNE experiment. In the presence of a CP-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 εμτ across both the NO and IO scenarios. We emphasize that among all the experiments considered, NOνA 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 CP-violating phase. Our results hint at a possible imprint of new physics in neutrino oscillations.
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.
Neutrino oscillations can be efficiently simulated on a quantum computer using the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) theory in close analogy to the physical processes realized in experiments. We simulate three-flavor neutrino oscillations on a two-qubit NMR quantum information processor. The three-flavor neutrino states were encoded into the two-qubit system, leaving one redundant basis state (representing an unphysical sterile neutrino). We simulated the neutrino oscillations in different scenarios, including propagation in vacuum and through surrounding matter, and both with and without a CP violating phase δ at a Deep Underground Neutrino Experiment (DUNE) baseline distance of L = 1285 km. The oscillation probabilities were obtained after unitarily time evolving the initial flavor state and and comparisons were performed between different scenarios. Further, we design and implement an optimized quantum circuit encoding all four parameters (three mixing angles-θ12,θ23,θ13 and one complex phase δ) to implement the PMNS unitary matrix, which relates the flavor and mass eigenstates. The interaction with matter is considered as a perturbation to the vacuum Hamiltonian, and the same quantum circuit is employed with an approximation of two mixing angles (θ12 and θ13 ) and mass eigenvalues. Our experimental results match well with numerical simulations and highlight the potential of quantum computers for exploring the physics of neutrino oscillations.
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 simulate three-flavor neutrino oscillations on two-qubit quantum circuits. The flavor space is embedded as ∣00⟩=νe, ∣01⟩=νμ, ∣10⟩=ντ with the ∣11⟩ channel kept inert, and the input mixing parameters (NuFIT~5.3, normal ordering, with SK-atm) follow the global fit. We verify three physical settings against analytic or exact references: vacuum propagation, reproduced by a mass-eigenstate phase circuit to ∼10−16; constant-density Mikheev--Smirnov--Wolfenstein (MSW) matter effects, showing resonant flavor conversion when the matter potential A crosses Δm312; and varying-density (supernova shock-shell) propagation by slicing plus second-order Suzuki--Trotter splitting, with per-slice Trotter error ∼10−6 and total accuracy ∼10−4 against the continuous profile. We report a Suzuki--Trotter precision--resource calibration varying order, step number, and matrix/probability error. It delimits brute-force Trotterization on solar baselines: we quantify both standard alternatives, coherence averaging and adiabatic MSW. We also compute quantum-information diagnostics from the same model parameters, namely mode entanglement and the CP asymmetry. Finally, we extend the framework to open quantum systems via a Lindblad master equation with dephasing and absorptive channels. These results provide a reproducible link between low-energy oscillation observables and quantum-information measures.
Neutrino flavor oscillations, a fundamental process in particle physics, involve the transition between different neutrino flavors, governed by a complex relationship between mass and flavor eigenstates. Traditionally, probabilistic measures are used to study neutrino oscillations, but recent research suggests that quantum complexity, specifically quantum spread complexity, offers deeper insights, especially regarding charge-parity (CP) violation. Our work shows that quantum complexity can predict CP-violating phases that align with experimental observations from T2K and NOvA. This approach provides a new connection between quantum information theory and particle physics, revealing the potential of complexity in neutrino studies.