Statistical properties of photon-added coherent state in a dissipative channel

We adopt a new approach (using the entangled state representation) to study time evolution of the mixed state in a dissipative channel (DC) with decay rate κ. We then investigate the statistical properties of the m-photon-added coherent state (PACS) in the DC, by deriving the analytical expressions of the Wigner function (WF), which turns out to be the Laguerre-Gaussian function. The criterion time for the definite positivity of WF: κt>κtc≡1/2 ln 2, valid for arbitrary m, is revealed. Time evolution of the photocount distribution is also derived analytically, which is related to two-variable Hermite polynomials. The tomogram of PACS is also calculated through the intermediate coordinate-momentum representation.