2005/12/29 by Michał Horodecki, Michal Horodecki, Jonathan Oppenheim +1 · 3 citations
Computer Science · Engineering · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Wireless Communication Security Techniques #quant-ph
paper · pdf · doi:10.1007/s00220-006-0118-x
published as Comm. Math. Phys. 269, 107 (2007) · 23 pages, 3 figures
arxiv created 2005/12/29 · openalex publication_date 2006/10/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.