Majorization theory approach to the Gaussian channel minimum entropy   conjecture
  A longstanding 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. 
Raul Garcia-Patron, Carlos Navarrete-Benlloch, Seth Lloyd, Jeffrey H.   Shapiro and Nicolas J. Cerf
quant-ph