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

Anura Abeyesinghe, Igor Devetak, Patrick Hayden, Andreas Winter

Research output: Contribution to journalArticlepeer-review

150 Scopus citations


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. This journal is

Original languageEnglish
Pages (from-to)2537-2563
Number of pages27
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2108
StatePublished - 8 Aug 2009
Externally publishedYes


  • Coding
  • Entanglement
  • Quantum information


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