Off-resonant preservation and generation of imaginarity in distributed scenarios

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.