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

Abeyesinghe, Anura and Devetak, Igor and Hayden, Patrick and Winter, Andreas (2009) The mother of all protocols: restructuring quantum information's family tree. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 465 (2108). pp. 2537-2563. ISSN 1364-5021.

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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.

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Additional Information:© 2009 The Royal Society. Received April 16, 2009. Accepted May 1, 2009. The authors thank Debbie Leung for bringing to their attention the possibility of replacing Haar measure unitaries with random Clifford group elements. They also thank Isaac Chuang, Ignacio Cirac, Frédéric Dupuis, Renato Renner and Jürg Wullschleger for their helpful comments. A.A. appreciates the support of the US National Science Foundation through grant no. EIA-0086038. I.D. was partially supported by the NSF under grant no. CCF-0524811. P.H. was supported by the Canada Research Chairs program, the Canadian Institute for Advanced Research, and Canada’s NSERC. He is also grateful to the Benasque Centre for Science and CQC Cambridge for their hospitality. A.W. was supported by the UK Engineering and Physical Sciences Research Council’s ‘IRC QIP’, and by the EC projects RESQ (contract IST-2001-37759) and QAP (contract IST-2005-15848), as well as by a University of Bristol Research Fellowship.
Funding AgencyGrant Number
Canada Research Chairs programUNSPECIFIED
Canadian Institute for Advanced ResearchUNSPECIFIED
Natural Sciences and Engineering Research Council of CanadaUNSPECIFIED
Engineering and Physical Sciences Research Council (UK)UNSPECIFIED
European CommissionIST-2001-37759
European CommissionIST-2005-15848
University of BristolUNSPECIFIED
Subject Keywords:quantum information; coding; entanglement
Issue or Number:2108
Record Number:CaltechAUTHORS:20090730-094057970
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14737
Deposited By: Jason Perez
Deposited On:07 Aug 2009 18:04
Last Modified:03 Oct 2019 00:52

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