The classical diffusion equation is [1] where \(\kappa \) is the diffusion rate, thus what is the corresponding quantum diffusion equation? Using the P-representation of the density operator \(\rho \) , i.e., \(\rho =\pi ^{-1}\int \) d \(^{2}z\) P \((z)|z\rangle \langle z|\) , thus the time-evolution of the density operator \(\rho \) satisfies the equation