Solution to time-energy costs of quantum channels
  We derive a formula for the time-energy costs of general quantum channels proposed in [Phys. Rev. A 88, 012307 (2013)]. This formula allows us to numerically find the time-energy cost of any quantum channel using positive semidefinite programming. We also derive a lower bound to the time-energy cost for any channels and the exact the time-energy cost for a class of channels which includes the qudit depolarizing channels and projector channels as special cases. 
Chi-Hang Fred Fung and H. F. Chau and Chi-Kwong Li and Nung-Sing Sze
quant-ph