Quantum speed limit time for bipartite entanglement in neutrino oscillations in matter with non-standard interactions

In the three-flavor neutrino oscillation framework, we investigate the transition probabilities of an initial muon neutrino flavor state in the presence of non-standard interactions (NSIs) characterized by complex off-diagonal ($|ε_{αβ}|e^{iϕ_{αβ}}$) and diagonal parameters ($|ε_{αα}-ε_{ββ}|$), 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, NO$ν$A, 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 $ε_{μτ}$ across both the NO and IO scenarios. We emphasize that among all the experiments considered, NO$ν$A 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.

💡 Research Summary

In this work the authors explore the quantum‑information aspects of three‑flavor neutrino oscillations in matter, focusing on how non‑standard interactions (NSI) and the CP‑violating phase affect the generation and decay of bipartite mode entanglement and the associated quantum speed limit (QSL) time. Starting from the standard PMNS framework, they add a constant matter potential VCC and a generic NSI Hamiltonian characterized by complex off‑diagonal parameters εαβ=|εαβ|e^{iϕαβ} and diagonal differences |εαα−εββ|. The total Hamiltonian Htot=HSO+HNSI is time‑independent, allowing the unitary evolution |Ψ(t)⟩=e^{-iHtot t}|Ψ(0)⟩ of an initial muon‑flavor neutrino state.

The authors map the three flavor modes onto two virtual qubits (mode entanglement) and define the reduced density matrix ρ1 by tracing over one subsystem. From the eigenvalues ηi of ρ1 they compute the entanglement entropy SEE=−∑i ηi log2 ηi and the capacity of entanglement CE=∑i ηi (log2 ηi)^2−SEE^2, the latter quantifying fluctuations of the entropy. The QSL time for bipartite entanglement is then expressed as

 TEQSL = |SEE(T)−SEE(0)| /