Entropy evolution law of general quadratic state in a laser channel

Using the integration within ordered products, we obtain the analytical density-operator evolution of the general quadratic state ρ 0 in a laser channel, which always maintains the same form as the initial density operator ρ 0. Introducing the differential representation of the von-Neumann entropy and two important resemble formulas, we analytically and numerically investigate the entropy evolution of the state ρ 0 in a laser channel, which is determined by not only the competition of the gain and loss of the laser channel, but also the coefficients α, β of the initial quadratic state ρ 0.