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