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Quantum State Merging and Negative Information

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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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Authors and Affiliations

  1. Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952, Gdańsk, Poland

    Michał Horodecki

  2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, U.K.

    Jonathan Oppenheim

  3. Department of Mathematics, University of Bristol, Bristol, BS8 1TW, U.K.

    Andreas Winter

Authors
  1. Michał Horodecki
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  2. Jonathan Oppenheim
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  3. Andreas Winter
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Corresponding author

Correspondence to Jonathan Oppenheim.

Additional information

Communicated by M. B. Ruskai

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Horodecki, M., Oppenheim, J. & Winter, A. Quantum State Merging and Negative Information. Commun. Math. Phys. 269, 107–136 (2007). https://doi.org/10.1007/s00220-006-0118-x

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  • DOI: https://doi.org/10.1007/s00220-006-0118-x

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