Off-resonant preservation and generation of imaginarity in distributed scenarios

TL;DR

This work addresses how to preserve and generate quantum imaginarity resources—NAQI and DIA—in distributed two-qubit systems coupled to a lossy cavity. By solving the exact dynamics beyond Born-Markov and analyzing both resonant and off-resonant (dispersive) regimes, it shows that large symmetric detuning can markedly extend the lifetime of these resources, while off-resonant interactions can generate high NAQI and DIA from product states through cavity-mediated effective coupling. The results provide physical intuition via dispersive coupling and quantify optimal detuning and coupling conditions, offering practical guidance for maintaining imaginarity in open quantum systems. The findings have potential implications for remote quantum information tasks that rely on imaginarity as a resource and motivate further exploration of active protection and multi-reservoir scenarios.

Abstract

We study the nonlocal advantage of quantum imaginarity (NAQI) and distillable imaginarity of assistance (DIA), which treat imaginarity as a resource in distributed scenarios. For two qubits interacting with a lossy cavity, it is shown that both the NAQI and DIA can be well preserved for long times in the presence of large and symmetric detuning between the qubits and the cavity. Moreover, the off-resonant interaction generates a high degree of NAQI and DIA from the initial product states of two qubits having the same detunings and unequal couplings to the cavity. Based on the effective coupling of the qubits induced by the cavity mode, we explain the physical mechanism underlying the validity of this strategy. Our findings shed light on the role that off-resonant interactions have in the efficient control of imaginarity in distributed scenarios.

Figures (9)

• Figure 1: Illustration of the imaginarity steering procedure in distributed scenarios, where the duo Alice ($A$) and Bob ($B$) share a two-qubit state $\rho_{AB}$ in prior. (a) The NAQI on qubit $B$ achieved by LOCC. (b) The assisted imaginarity distillation on qubit $B$ by LQRCC.
• Figure 2: $\mathcal{N}_{tr}(\rho_{AB})$ versus $\lambda t$ for the initial state $|\Psi^{+}\rangle$ with different $R$ and $r_A$, where the solid black, dashed red, dash-dotted blue, and dotted green lines correspond to $\delta=0$, $10\lambda$, $20\lambda$, and $30\lambda$, respectively. The horizontal dashed lines show the bound $\mathcal{I}_{tr,\mathcal{B}}$ larger than which there is trace norm of NAQI in $\rho_{AB}$.
• Figure 3: $\mathcal{N}_{re}(\rho_{AB})$ versus $\lambda t$ for the initial state $|\Psi^{+}\rangle$ with different $R$ and $r_A$, where the solid black, dashed red, dash-dotted blue, and dotted green lines correspond to $\delta=0$, $10\lambda$, $20\lambda$, and $30\lambda$, respectively. The horizontal dashed lines show the bound $\mathcal{I}_{re,\mathcal{B}}$ larger than which there is relative entropy of NAQI in $\rho_{AB}$.
• Figure 4: $\mathcal{N}_g(\rho_{AB})$ versus $\lambda t$ for the initial state $|\Psi^{+}\rangle$ with different $R$ and $r_A$, where the solid black, dashed red, dash-dotted blue, and dotted green lines correspond to $\delta=0$, $10\lambda$, $20\lambda$, and $30\lambda$, respectively. The horizontal dashed lines show the bound $\mathcal{I}_{g, \mathcal{B}}$ larger than which there is geometric NAQI in $\rho_{AB}$.
• Figure 5: $\mathcal{N}_{tr}(\rho_{AB})$ versus $\lambda t$ for the initial state $|\Psi^{+}\rangle$ with $r_A= \sqrt{2}/2$ and different $R$, $\delta_A$, and $\delta_B$. The solid black, dashed red, and dash-dotted blue lines in (a) and (b) [(c)--(f)] are plotted for $\delta_B=0$, $10\lambda$, and $20\lambda$ [$\delta_B=-\delta_A$, $0$, and $\delta_A$], respectively.