Threshold <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>P</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> distillation of multipartite quantum correlations

We introduce a threshold quantum distillation protocol that enables the extraction of perfect quantum correlations from multiple imperfect copies of a multipartite quantum state using only a subset of the parties ( Q < P ) in the network. In particular, we show that for high-dimensional Greenberger–Horne–Zeilinger states, entanglement can be distilled by local filtering operations applied by just a single party, independent of the total number of parties in the network. In contrast, for the W states, at least P − 1 parties are required for successful distillation, highlighting a strong connection between distillability and separability. We provide explicit protocols for threshold entanglement distillation and threshold steering distillation (TSD), and establish a direct link between the two: Any assemblage that can be distilled via TSD necessarily corresponds to a distillable entangled state. Our framework introduces a scalable and experimentally viable approach to distillation in quantum networks, with potential applications in distributed quantum computing, communication, and cryptography.