Partial quantum information.

Abstract:

:Information--be it classical or quantum--is measured by the amount of communication needed to convey it. In the classical case, if the receiver has some prior information about the messages being conveyed, less communication is needed. Here we explore the concept of prior quantum information: given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the partial information one system needs, conditioned on its prior information. We find that it is given by the conditional entropy--a quantity that was known previously, but lacked an operational meaning. In the classical case, partial information must always be positive, but we find that in the quantum world this physical quantity can be negative. If the partial information is positive, its sender needs to communicate this number of quantum bits to the receiver; if it is negative, then sender and receiver instead gain the corresponding potential for future quantum communication. We introduce a protocol that we term 'quantum state merging' which optimally transfers partial information. We show how it enables a systematic understanding of quantum network theory, and discuss several important applications including distributed compression, noiseless coding with side information, multiple access channels and assisted entanglement distillation.

journal_name

Nature

journal_title

Nature

authors

Horodecki M,Oppenheim J,Winter A

doi

10.1038/nature03909

keywords:

subject

Has Abstract

pub_date

2005-08-04 00:00:00

pages

673-6

issue

7051

eissn

0028-0836

issn

1476-4687

pii

nature03909

journal_volume

436

pub_type

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