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Photonic GHZ states serve as the central resource for a number of important applications in quantum information science, including secret sharing, sensing, and fusion-based quantum computing. The use of photon-emitter entangling gates is a promising approach to creating these states that sidesteps many of the difficulties associated with intrinsically probabilistic methods based on linear optics. However, the efficient creation of high-fidelity GHZ states of many photons remains an outstanding challenge due to both coherent and incoherent errors during the generation process. Here, we propose an entanglement concentration protocol that is capable of generating perfect GHZ states using only local gates and measurements on imperfect weighted graph states. We show that our protocol is both efficient and robust to incoherent noise errors.

Time-crystalline behavior has been predicted and observed in quantum central-spin systems with periodic driving and Ising interactions. Here, we theoretically show that it can also arise in central-spin systems with Heisenberg interactions. We present two methods to achieve this: application of a sufficiently large Zeeman splitting on the central spin compared to the satellite spins, or else by applying additional pulses to the central spin every Floquet period. In both cases, we show that the system exhibits a subharmonic response in spin magnetizations in the presence of disorder for both pure Heisenberg and XXZ interactions. Our results pertain to any XXZ central-spin system, including hyperfine-coupled electron-nuclear systems in quantum dots or color centers.