Dephasing Effects on the Dynamical Evolution of Quantum Correlations and Coherence in Neutrino Oscillations

Abstract: Neutrino oscillations confirm the presence of mode entanglement, as each flavor eigenstate is composed of a coherent superposition of distinct mass eigenstates. In this work, we investigate the dynamics of quantum resources in neutrino oscillation systems by analyzing quantum steering, logarithmic negativity, and quantum coherence within a two-flavor framework. Treating neutrino oscillations as an effective two-level quantum system, we study the influence of environmental decoherence on these nonclassical features by modeling the system as an open quantum system. Three representative noise channels are considered, namely amplitude damping (AD), phase flip (PF), and phase damping (PD), allowing us to capture both dissipative and dephasing mechanisms. We examine the evolution of quantum resources in both Markovian and non-Markovian regimes, highlighting the role of memory effects in the system-environment interaction. The results reveal a clear hierarchy in the robustness of quantum resources under decoherence. Steering is the most sensitive correlation in the hierarchy under decoherence effects. while logarithmic negativity exhibits intermediate robustness. Quantum coherence displays the highest resilience, persisting over a wider range of parameters. In the PF and PD channels, logarithmic negativity and coherence are shown to exhibit identical dynamical behavior, reflecting their common dependence on phase-related noise. In contrast, the non-Markovian regime leads to delayed decoherence and partial revivals of entanglement and coherence due to information backflow, whereas quantum steering remains strongly suppressed. These findings provide a comparison of different quantum resources in neutrino oscillation systems and offer new insights into the interplay between decoherence mechanisms and quantum correlations.

• The paper demonstrates that quantum steering, entanglement, and coherence exhibit distinct robustness when subjected to various decoherence channels in neutrino oscillations.
• It employs a two-level open quantum system model with local Kraus operators to simulate amplitude damping, phase flip, and phase damping effects, yielding analytic and numerical insights.
• Results indicate non-Markovian dynamics enable partial resource revivals, underscoring the potential for exploiting environmental memory in experimental neutrino physics.

Dephasing Effects on Quantum Correlations and Coherence in Neutrino Oscillations

Overview

This paper develops a theoretical and numerical investigation into the dynamics of quantum information-theoretic resources—EPR steering, logarithmic negativity, and $l_1$-norm coherence—in the context of neutrino oscillations modeled as two-level open quantum systems. The study systematically analyzes how amplitude damping (AD), phase flip (PF), and phase damping (PD) noise channels affect the evolution and robustness of these resources in both Markovian and non-Markovian regimes. By mapping flavor oscillations onto an effective two-qubit Hilbert space, the work establishes connections between quantum resource theory and particle physics, specifically focusing on the effects of environmental decoherence and memory on nonclassical features inherent to neutrino flavor conversion.

Theoretical Model: Neutrino Oscillations as a Quantum Resource Platform

Under the two-flavor approximation, neutrino oscillations are interpreted within the framework of quantum information, leveraging the formal analogy between superpositions of flavor and mass eigenstates and single-particle mode entanglement. The PMNS mixing matrix translates the temporal evolution of a definite flavor state into an entangled superposition in the occupation number basis, giving rise to Bell-like states in the bipartite (flavor) qubit space. Oscillation parameters such as the mixing angle and mass squared differences define the oscillatory phase $\phi$, establishing the dependence of survival and transition probabilities, and thereby the degree of quantum correlation, on experimentally measurable quantities. The two-qubit density matrix retains an $X$-state structure, conducive for analytic evaluation of steering, entanglement, and coherence measures under various noisy channels.

Quantification of Quantum Resources

• EPR Steering: The directional steering measures $\mathcal{S}_{A \to B}$ and $\mathcal{S}_{B \to A}$ are computed using normalized entropic inequalities built from marginal and joint probabilities of local Pauli measurements. The hierarchy of nonclassical correlations dictates that steerability implies entanglement but not vice versa, making steering maximally sensitive to decoherence.
• Logarithmic Negativity: The entanglement quantifier used is the logarithmic negativity, derived from the trace norm of the partial transpose of the two-qubit density matrix. This measure is operationally computable for general mixed states and directly tracks the entanglement evolution under noisy dynamics.
• Quantum Coherence: The $l_1$-norm, summing the off-diagonal density matrix elements, quantifies the basis-dependent coherence responsible for interference in oscillation phenomena and provides a lower rung on the resource hierarchy but exhibits notable resilience against certain noise types.

Open Quantum System Dynamics and Noise Channels

The evolution under environmental influence is modeled using local Kraus operators for three paradigmatic channels:

• Amplitude Damping (AD): Models energy dissipation, irreversibly reducing excited-state populations. Both coherence and entanglement are suppressed, with steering most adversely impacted.
• Phase Flip (PF): Induces random $\sigma_z$ flips, generating pure dephasing. Populations remain unchanged; off-diagonal coherence and entanglement decay symmetrically but may undergo revivals under non-Markovianity.
• Phase Damping (PD): Pure dephasing with no population transfer, leading to exponential decay of coherence elements; populations are invariant.

Markovian evolution (short correlation times) results in monotonic decay, while non-Markovianity (long correlation times, significant environment memory) induces information backflow, leading to partial revivals of quantum resources.

Numerical Analysis and Resource Hierarchy

Using empirically determined oscillation parameters from KamLAND, Daya Bay, MINOS, T2K, and JUNO, the paper presents detailed numerical results for each experiment under all noise channels. The analysis yields several robust trends:

1. Hierarchy of Robustness: Steering $<$ Entanglement $<$ Coherence under all channels. Steering is highly fragile and the first resource destroyed by noise, with entanglement and especially coherence persisting much longer.
2. Channel-Specific Dynamics:
   • AD induces monotonic decay for all resources.
   • PF and PD channels yield identical decay behavior for entanglement and coherence—both show symmetric decay and revival under PF due to phase noise symmetry, but linear decay under PD.
   • Steering remains more sensitive than either entanglement or coherence, vanishing at smaller decoherence strengths.
3. Markovian versus Non-Markovian Regimes:
   • Markovian: All resources experience uniform, irreversible decay.
   • Non-Markovian: Delayed decoherence and revivals for entanglement and coherence; steering remains suppressed, with backflow less able to restore it compared to other resources.
4. Experiment-Dependent Effects: KamLAND displays the greatest resilience for all resources, while configurations such as JUNO show maximal sensitivity to decoherence, which aligns with the specific oscillation parameters and baselines.

Implications for Fundamental Physics and Quantum Technologies

This comprehensive mapping of resource evolution under realistic noise models advances the fundamental understanding of quantum information-theoretic phenomena in particle physics. Key implications include:

• Fundamental Perspective: The reduction of quantum resource hierarchies by environmental noise underscores the fragility of genuine nonlocal effects (steering) in practical settings and highlights the distinctive resilience of quantum coherence.
• Experimental Outlook: As direct measurement of quantum correlations in neutrino systems remains elusive, these results inform indirect reconstruction protocols and motivate more sensitive analyses seeking signatures of nonclassicality in oscillation data.
• Theoretical Advancement: The identification of identical dynamics for entanglement and coherence under PF and PD enriches the study of quantum resource interconversion and may inspire analogous strategies for enhanced quantum information protocols.
• Non-Markovian Control: The observed revivals due to non-Markovianity suggest avenues for designing systems or experiments that can exploit environmental memory to prolong useful quantum correlations in open-system platforms.

Future Directions

Further research may extend to:

• Three-flavor oscillation scenarios, incorporating CP-violating effects.
• Integration of more complex noise models (e.g., colored noise, turbulence-induced decoherence (Bao et al., 28 Jan 2026)).
• Explicit device-independent tests for quantum correlations in neutrino data.
• Quantum resource dynamics in other particle oscillation phenomena or cosmological neutrino backgrounds.

Conclusion

This study rigorously establishes the response of steering, entanglement, and coherence in neutrino oscillations to paradigmatic environmental decoherence processes. The resultant hierarchy of robustness and detailed channel-dependent dynamics underpin a refined understanding of quantum resource persistence in relativistic open quantum systems, contributing a valuable bridge between quantum information science and high-energy particle physics (2605.05015).