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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• Quantum discord as a resource in quantum communication
• Entangled black holes as ciphers of hidden information
• Approximate quantum error correction, random codes, and quantum channel capacity
• Duality of privacy amplification against quantum adversaries and data compression with quantum side information
• On the distributed compression of quantum information
• Quantum Information Complexity and Amortized Communication
• Multiparty quantum protocols for assisted entanglement distillation
• Pseudo-randomness and Learning in Quantum Computation
• The black hole information problem beyond quantum theory
• Distributed Compression and Squashed Entanglement
• Channel simulation with quantum side information
• A random-coding based proof for the quantum coding theorem