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Quantum information theory is a multidisciplinary field whose objective is tounderstand what happens when information is stored in the state of a quantumsystem. Quantum mechanics provides us with a new resource, called quantumentanglement, which can be exploited to achieve novel tasks such asteleportation and superdense coding. Current technologies allow thetransmission of entangled photon pairs across distances up to roughly 100kilometers. For longer distances, noise arising from various sources degradethe transmission of entanglement to the point that it becomes impossible to usethe entanglement as a resource for future tasks. A strategy for dealing withthis difficulty is to employ quantum repeaters, stations intermediate betweenthe sender and receiver which participate in the process of entanglementdistillation, thereby improving on what the sender and receiver could do ontheir own. In this work, we study entanglement distillation between tworecipients sharing a mixed state and with the help of repeater stations. Weextend the notion of entanglement of assistance to arbitrary states and give aprotocol for extracting pure entanglement. We also study quantum communicationprotocols in a more general context. We give a new protocol for the task ofmultiparty state merging. The previous multiparty state merging protocolrequired the use of time-sharing. Our protocol does not require time-sharingfor distributed compression of two senders. In the one-shot regime, we achievemultiparty state merging with entanglement costs not restricted to cornerpoints of the entanglement cost region. Our analysis of the entanglement costis performed using (smooth) min- and max-entropies. We illustrate the benefitsof our approach by looking at different examples.

Multiparty quantum protocols for assisted entanglement distillation