Quantum state merging and negative information

M Horodecki, J Oppenheim, AJ Winter

Research output: Contribution to journalArticle (Academic Journal)peer-review

209 Citations (Scopus)


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.
Translated title of the contributionQuantum state merging and negative information
Original languageEnglish
Pages (from-to)107 - 136
Number of pages30
JournalCommunications in Mathematical Physics
Volume269 (1)
Publication statusPublished - Jan 2007

Bibliographical note

Publisher: Springer


Dive into the research topics of 'Quantum state merging and negative information'. Together they form a unique fingerprint.

Cite this