Communications in Mathematical Physics

, Volume 269, Issue 1, pp 107–136

Quantum State Merging and Negative Information

  • Michał Horodecki
  • Jonathan Oppenheim
  • Andreas Winter
Article

Abstract

We consider a quantum state shared between many distant locations, and define a quantum information processing primitive, state merging, that optimally merges the state into one location. As announced in [Horodecki, Oppenheim, Winter, Nature 436, 673 (2005)], the optimal entanglement cost of this task is the conditional entropy if classical communication is free. Since this quantity can be negative, and the state merging rate measures partial quantum information, we find that quantum information can be negative. The classical communication rate also has a minimum rate: a certain quantum mutual information. State merging enabled one to solve a number of open problems: distributed quantum data compression, quantum coding with side information at the decoder and sender, multi-party entanglement of assistance, and the capacity of the quantum multiple access channel. It also provides an operational proof of strong subadditivity. Here, we give precise definitions and prove these results rigorously.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Michał Horodecki
    • 1
  • Jonathan Oppenheim
    • 2
  • Andreas Winter
    • 3
  1. 1.Institute of Theoretical Physics and AstrophysicsUniversity of GdańskGdańskPoland
  2. 2.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeU.K.
  3. 3.Department of MathematicsUniversity of BristolBristolU.K.

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