Generation of genuine all-way entanglement in defect-nuclear spin systems through dynamical decoupling sequences

Creating electron-nuclear entanglement in defects is difficult as the always-on hyperfine interactions prohibit complete isolation of the target system from unwanted spins. We design sequential or single-shot entangling gates that prepare high-quality GHZ_M states with minimal cross-talk and within the coherence times. We verify genuine multipartite correlations through the all-way entangling power of the gates. We study the entanglement of mixed electron-nuclear states and develop a non-unitary M-way entangling power which captures correlations arising from spectator nuclei.