Majorization Theory Approach to the Gaussian Channel Minimum Entropy Conjecture

• Main Authors: Garcia-Patron Sanchez, Raul (Contributor), Navarrete-Benlloch, Carlos (Contributor), Lloyd, Seth (Contributor), Shapiro, Jeffrey H. (Contributor), Cerf, Nicolas J. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor), Massachusetts Institute of Technology. Department of Mechanical Engineering (Contributor), Massachusetts Institute of Technology. Research Laboratory of Electronics (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society, 2012-07-17T12:43:02Z.
• Subjects: Article
• Online Access: Get fulltext

A long-standing open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding of coherent states using an isotropic Gaussian distribution in phase space. We show that proving a Gaussian minimum entropy conjecture for a quantum-limited amplifier is actually sufficient to confirm this capacity conjecture, and we provide a strong argument towards this proof by exploiting a connection between quantum entanglement and majorization theory.
Alexander von Humboldt-Stiftung
Belgian National Foundation for Scientific Research
European Union (Project No. FIS2008-06024-C03-01)
W. M. Keck Foundation Center for Extreme Quantum Information Theory
Spain. Ministerio de Ciencia e Innovación (MICINN) (FPU)
United States. Office of Naval Research (Basic Research Challenge Program)
Fondation pour la recherche strategique (France) (HIPERCOM)