  Entanglement is a key resource for quantum information technologies ranging
from quantum sensing to quantum computing. Conventionally, the entanglement
between two coupled qubits is established at the time scale of the inverse of
the coupling strength. In this work, we study two weakly coupled non-Hermitian
qubits and observe entanglement generation at a significantly shorter time
scale by proximity to a higher-order exceptional point. We establish a
non-Hermitian perturbation theory based on constructing a biorthogonal complete
basis and further identify the optimal condition to obtain the maximally
entangled state. Our study of speeding up entanglement generation in
non-Hermitian quantum systems opens new avenues for harnessing coherent
nonunitary dissipation for quantum technologies.
