Decoherence and evolution of a general quadratic state for amplitude decay

Making full use of the operator ordering method and the integration within ordered products, we obtain the analytical evolution law of a general quadratic state in the amplitude decay channel, and find that it is determined not only by the decay rate of the amplitude decay channel but also by the coefficients of the initial quadratic state. Further, the quantum statistical properties of the initial quadratic state for amplitude decay are investigated via its average photon number and photon-counting distribution, and its Wigner distribution function evolution is discussed in detail.