The mother of all protocols: Restructuring quantum information's family tree

Abstract

We give a simple, direct proof of the "mother" protocol of quantum information theory. In this new formulation, it is easy to see that the mother, or rather her generalization to the fully quantum Slepian-Wolf protocol, simultaneously accomplishes two goals: quantum communication-assisted entanglement distillation, and state transfer from the sender to the receiver. As a result, in addition to her other "children," the mother protocol generates the state merging primitive of Horodecki, Oppenheim and Winter, a fully quantum reverse Shannon theorem, and a new class of distributed compression protocols for correlated quantum sources which are optimal for sources described by separable density operators. Moreover, the mother protocol described here is easily transformed into the so-called "father" protocol whose children provide the quantum capacity and the entanglement-assisted capacity of a quantum channel, demonstrating that the division of single-sender/single-receiver protocols into two families was unnecessary: all protocols in the family are children of the mother.

25 pages, 6 figures

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Cited by in corpus (8)

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• Unbounded violation of tripartite Bell inequalities
• Entangled black holes as ciphers of hidden information
• Approximate quantum error correction, random codes, and quantum channel capacity
• On the distributed compression of quantum information
• Distributed Compression and Squashed Entanglement
• Channel simulation with quantum side information
• A random-coding based proof for the quantum coding theorem