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

TL;DR

The paper investigates how non-standard neutrino interactions (NSI) and a CP-violating phase affect the quantum-information aspects of three-flavor neutrino oscillations in matter, by analyzing bipartite entanglement and its quantum speed limit (QSL). Using mode entanglement, it expresses the entanglement entropy $S_{EE}$ and capacity of entanglement $C_E$ in terms of observable transition probabilities and derives the QSL bound $T^E_{\mathrm{QSL}}$ for the evolution of entanglement, incorporating the Hamiltonian variance $\Delta\mathcal{H}$. The authors map the flavor state to a three-qubit system, compute reduced states, and study $S_{EE}$, $C_E$, and $\tau^E_{\mathrm{QSL}}$ for NO and IO across T2K, NOvA, and DUNE, revealing that the off-diagonal NSI parameter $\varepsilon_{\mu\tau}$ produces the most pronounced effects, with NOvA and DUNE showing significant NSI-induced speed-up or suppression of entanglement evolution. The work finds that entanglement can reach maximal Bell-like states at specific baselines, and that DUNE exhibits the strongest NSI sensitivity in the QSL context, implying potential new-physics imprints in neutrino oscillations and informing CP-violation and mass-ordering studies.

Abstract

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.

Figures (11)

• Figure 1: From top to bottom, the left, middle, and right panels show the three-flavor transition probabilities $P({\nu_\mu\rightarrow \nu_e})$, $P({\nu_\mu\rightarrow \nu_\mu})$, and $P({\nu_\mu\rightarrow \nu_\tau})$, respectively, as functions of the baseline length $L\,\text{(km)}$ of the initial muon-flavor neutrino state $\ket{\nu_\mu}$, evolved under four scenarios: SO+NO (purple solid line), SO+IO (red dot-dashed line), NSI+NO (green dashed line), and NSI+IO (blue dotted line), using the best-fit CP-violating phases $\delta_{\rm CP}$ in NO ($\delta_{\rm CP}=177^{o}$) and IO ($\delta_{\rm CP}= 285^{o}$). The transition probabilities are compared across these scenarios for the off-diagonal NSI parameter $\left|\epsilon_{\mu\tau}\right|$ with complex phase $\phi_{\mu\tau}$, evaluated at the baselines and energies of the T2K (top row), NO$\nu$A (middle row), and DUNE (bottom row) experiments. The SO and NSI parameters used are taken from Tables \ref{['Tab1']} and \ref{['Tab2']}, respectively.
• Figure 2: From top to bottom, the left, middle, and right panels show the three-flavor transition probabilities $P({\nu_\mu\rightarrow \nu_e})$, $P({\nu_\mu\rightarrow \nu_\mu})$, and $P({\nu_\mu\rightarrow \nu_\tau})$, respectively, as functions of the baseline length $L\,\text{(km)}$ of the initial muon-flavor neutrino state $\ket{\nu_\mu}$, evolved under four scenarios: SO+NO (purple solid line), SO+IO (red dot-dashed line), NSI+NO (green dashed line), and NSI+IO (blue dotted line), using the best-fit CP-violating phases $\delta_{\rm CP}$ in NO ($\delta_{\rm CP}=177^{o}$) and IO ($\delta_{\rm CP}= 285^{o}$). The transition probabilities are compared across these scenarios for the diagonal NSI parameter $\left |\epsilon_{ee}-\epsilon_{\mu\mu}\right |$, evaluated at the baselines and energies of the T2K (top row), NO$\nu$A (middle row), and DUNE (bottom row) experiments. The SO and NSI parameters used are taken from Tables \ref{['Tab1']} and \ref{['Tab3']}, respectively.
• Figure 3: From top to bottom, the left panels show the entanglement entropy ($S_{EE}$) and capacity of entanglement ($C_{E}$), while the right panels show the QSL time for bipartite entanglement ($\tau^E_{\rm QSL}$), as functions of the baseline length $L\,\text{(km)}$ of the initial muon-flavor neutrino state $\ket{\nu_\mu}$, evolved under four scenarios: SO+NO (purple solid line), SO+IO (red dot-dashed line), NSI+NO (green dashed line), and NSI+IO (blue dotted line), using the best-fit CP-violating phases $\delta_{\rm CP}$ in NO ($\delta_{\rm CP}=177^{o}$) and IO ($\delta_{\rm CP}= 285^{o}$). The $S_{EE}$, $C_{E}$, and $\tau^E_{\rm QSL}$ are compared across these scenarios for the off-diagonal NSI parameter $\left|\epsilon_{\mu\tau}\right|$ with complex phase $\phi_{\mu\tau}$, evaluated at the baselines and energies of the T2K (top row), NO$\nu$A (middle row), and DUNE (bottom row) experiments. The SO and NSI parameters used are taken from Tables \ref{['Tab1']} and \ref{['Tab2']}, respectively.
• Figure 4: From top to bottom, the panels display the oscillogram plots of the entanglement entropy ($S_{EE}$) in a bipartite system for the initial muon-flavor neutrino state $\ket{\nu_\mu}$, as functions of the baseline length $L\,\text{(km)}$ and the whole range of CP-violating phase $\delta_{CP}$ ($0^\circ \leq \delta_{\rm CP}\leq 360^\circ$), under four scenarios: SO+NO (upper left panel), SO+IO (upper right panel), NSI+NO (lower left panel), and NSI+IO (lower right panel). The $S_{EE}$ is shown for the off-diagonal NSI parameter $\left|\epsilon_{\mu\tau}\right|$ with complex phase $\phi_{\mu\tau}$, evaluated at the baseline and energy of the DUNE experiment. The SO and NSI parameters used are taken from Tables \ref{['Tab1']} and \ref{['Tab2']}, respectively.
• Figure 5: From top to bottom, the left panels show the entanglement entropy ($S_{EE}$) and capacity of entanglement ($C_{E}$), while the right panels show the QSL time for bipartite entanglement ($\tau^E_{\rm QSL}$), as functions of the baseline length $L\,\text{(km)}$ of the initial muon-flavor neutrino state $\ket{\nu_\mu}$, evolved under four scenarios: SO+NO (purple solid line), SO+IO (red dot-dashed line), NSI+NO (green dashed line), and NSI+IO (blue dotted line), using the best-fit CP-violating phases $\delta_{\rm CP}$ in NO ($\delta_{\rm CP}=177^{o}$) and IO ($\delta_{\rm CP}= 285^{o}$). The $S_{EE}$, $C_{E}$, and $\tau^E_{\rm QSL}$ are compared across these scenarios for the diagonal NSI parameter $\left |\epsilon_{ee}-\epsilon_{\mu\mu}\right |$, evaluated at the baselines and energies of the T2K (top row), NO$\nu$A (middle row), and DUNE (bottom row) experiments. The SO and NSI parameters used are taken from Tables \ref{['Tab1']} and \ref{['Tab3']}, respectively.