  For a dissipative channel governed by the master equation of density
operator}$d\rho /dt=\kappa \left(2a\rho a^{\dagger}-a^{\dagger}a\rho -\rho
a^{\dagger}a\right) ,${\small \ we find that photocount distribution formula at
time}$t,${\small \}$p\left(n,t\right) =Tr\left\{\rho \left(t\right)
\mathbf{\colon}\left(\xi a^{\dagger}a\right) ^{n}e^{-\xi a^{\dagger}a}/n!\colon
\right\} ,${\small \ becomes}$p\left(n,t\right) =Tr% \left[ \rho \left(0\right)
\mathbf{\colon}\left(\xi e^{-2\kappa t}a^{\dagger}a\right) ^{n}e^{-\xi
e^{-2\kappa t}a^{\dagger}a}/n!\colon % \right] ,${\small \ as if the quantum
efficiency}$\xi ${\small \ of the detector becomes}$\xi e^{-2\kappa t}${\ This
law greatly simplifies the theoretical study of photocount distribution for
quantum optical field.
