Majorization Theory Approach to the Gaussian Channel Minimum Entropy Conjecture
Raúl García−Patrón, Carlos Navarrete–Benlloch, Seth Lloyd, Jeffrey H. Shapiro, Nicolas J. Cerf · Physical Review Letters · 2012
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.