Minimum output entropy of bosonic channels: a conjecture
  The von Neumann entropy at the output of a bosonic channel with thermal noise is analyzed. Coherent-state inputs are conjectured to minimize this output entropy. Physical and mathematical evidence in support of the conjecture is provided. A stronger conjecture--that output states resulting from coherent-state inputs majorize the output states from other inputs--is also discussed. 
Vittorio Giovannetti, Saikat Guha, Seth Lloyd, Lorenzo Maccone, and   Jeffrey H. Shapiro