Partial quantum information

Michał Horodecki, Jonathan Oppenheim () and Andreas Winter
Additional contact information
Michał Horodecki: University of Gdańsk
Jonathan Oppenheim: University of Cambridge
Andreas Winter: University of Bristol

Nature, 2005, vol. 436, issue 7051, 673-676

Abstract: Abstract Information—be it classical1 or quantum2—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 needed3. 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.

Date: 2005
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.nature.com/articles/nature03909 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nat:nature:v:436:y:2005:i:7051:d:10.1038_nature03909

Ordering information: This journal article can be ordered from
https://www.nature.com/

DOI: 10.1038/nature03909

Access Statistics for this article

Nature is currently edited by Magdalena Skipper

More articles in Nature from Nature
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().