A family of quantum protocols

TL;DR

The paper studies rates for inter-conversion of quantum information resources and introduces two dual, purely quantum protocols—the 'mother' and 'father'—from which a large family of 'children' protocols can be derived via teleportation or super-dense coding. It uses a resource-inequality framework that couples dynamic resources (qubit channels) and static resources (ebits/noisy states) and reveals dual relationships between the mother and father. The authors further develop the concept of coherent communication, showing how to make protocols coherent to regenerate parents from children and linking these constructions to entanglement distillation and entanglement-assisted quantum communication results, including channel capacity and hashing inequalities. They argue that these constructions point toward optimal resource trade-offs and outline plans for a detailed treatment in future work.

Abstract

We introduce two dual, purely quantum protocols: for entanglement distillation assisted by quantum communication (``mother'' protocol) and for entanglement assisted quantum communication (``father'' protocol). We show how a large class of ``children'' protocols (including many previously known ones) can be derived from the two by direct application of teleportation or super-dense coding. Furthermore, the parent may be recovered from most of the children protocols by making them ``coherent''. We also summarize the various resource trade-offs these protocols give rise to.

Figures (1)

• Figure 1: The family tree: the dashed lines signify duality, and the dashed-dotted line is the almost-duality described in the text. The solid arrows signify descendance via (TP), (SD) or (QE).