Multiparty quantum protocols for assisted entanglement distillation

Nicolas Dutil

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.

Adrian Auer, René Schwonnek, Christian Schoder +3 more

Vlatko Vedral

Nicolas Dutil, Patrick M. Hayden

We present a protocol for performing state merging when multiple parties share a single copy of a mixed state, and analyze the entanglement cost in terms of min- and max-entropies. Our protocol allows for interpolation between corner points of the rate region without the need for time-sharing, a primitive which is not available in the one-shot setting. We also compare our protocol to the more naive strategy of repeatedly applying a single-party merging protocol one party at a time, by performing a detailed analysis of the rates required to merge variants of the embezzling states. Finally, we analyze a variation of multiparty merging, which we call split-transfer, by considering two receivers and many additional helpers sharing a mixed state. We give a protocol for performing a split-transfer and apply it to the problem of assisted entanglement distillation.

K. G. H. Vollbrecht, Frank Verstraete

We construct interesting entanglement distillation protocols by interpolating between the recurrence and hashing protocols. This leads to asymptotic two-way distillation protocols, resulting in an improvement of the distillation rate for all mixed Bell diagonal entangled states, even for the ones with very high fidelity. We also present a method for how entanglement-assisted distillation protocol can be converted into nonentanglement-assisted protocols with the same yield.

Ming-Jing Zhao, Ting-Gui Zhang, Xianqing Li-Jost +1 more