Threshold (Q, P) Quantum Distillation

Quantum distillation is the task of concentrating quantum correlations present in 'N' imperfect copies using free operations by involving all 'P' parties sharing the quantum correlations. We present a threshold quantum distillation task where the same objective is achieved but using fewer parties 'Q'. In particular, we give exact local filtering operations by the participating parties sharing a high-dimension multipartite GHZ or W state to distil the perfect quantum correlation. Specifically, an arbitrary GHZ state can be distilled using just one party in the network, as both the success probability of the distillation protocol and the fidelity after the distillation are independent of the number of parties. However, for a general W-state, at least 'P-1' parties are required for the distillation, indicating a strong relationship between the distillation and the separability of such states. Further, we connect threshold entanglement distillation and quantum steering distillation.