Experimental certification of the nonlocal advantages of quantum imaginarity

Abstract

Quantum imaginarity is a distinct resource in quantum information theory, yet its nonlocal properties have not been fully explored. Here, we report an experimental study of the nonlocal advantage of quantum imaginarity (NAQI), in which local measurements on one subsystem can steer the average imaginarity of the conditional states of the other subsystem beyond the corresponding classical bound. The $l_1$-norm of imaginarity inequality is adopted as an experimentally accessible witness. A hybrid optimization algorithm that combines a genetic algorithm with sequential quadratic programming is developed to avoid local optima and accelerate the search for optimal measurement settings. Using polarization-encoded photonic qubits, we prepare two classes of two-qubit Bell-diagonal states and experimentally characterize the imaginarity of the conditional states following local measurements. Clear violations of the $l_1$-norm of imaginarity inequality are observed, providing an experimental certification of NAQI. We further investigate the relationship among NAQI, the nonlocal advantage of quantum coherence (NAQC), and Bell nonlocality based on their respective inequality criteria. For the two-qubit Werner states considered in this work, the regions of states that violate the respective criteria satisfy $\mathcal{D}_{\rm NAQC}\subset\mathcal{D}_{\rm NAQI}\subset\mathcal{D}_{\rm BN}$. Our work provides an experimental realization of NAQI and a comparison of different forms of quantum nonclassicality in a photonic platform.