The entropy variation and quantum statistical behaviors of a general linear state in a laser channel

Using the integration within ordered products and the operator ordering method, we obtain the analytical evolution of the general linear normally ordered density operator and use it to investigate the entropy evolution of a general linear state in a laser channel. This entropy evolution is determined not only by the competition of the gain and loss of the channel but also by the coefficients of the initial linear state. The numerical results indicate that, as time progresses, the entropy either increases linearly or approaches a constant value, depending on the gain and loss of the laser channel. Additionally, we analyze the quantum statistical properties of a general linear state for laser noise through analytical and numerical methods. This includes examining the average photon number, photon counting distribution, and Wigner distribution function in detail.