Threshold (Q, P) Quantum Distillation

TL;DR

This paper introduces a threshold quantum distillation protocol that reduces the number of parties needed for perfect quantum correlation distillation from multipartite GHZ or W states, with implications for quantum network efficiency.

Contribution

It provides exact local filtering operations for distilling quantum correlations using fewer parties, highlighting differences between GHZ and W states and linking entanglement and steering distillation.

Findings

GHZ states can be distilled with a single party, independent of total parties.

W states require at least P-1 parties for distillation.

Distillation success probability and fidelity are independent of the number of parties for GHZ states.

Abstract

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.