Upper bound of the accessible information and lower bound of the Bayes cost in quantum signal-detection processes

Upper bound of the accessible information and lower bound of the Bayes cost in quantum detection processes for Gaussian state signals under the influence of thermal noise are derived by means of the superoperator representation of quantum stales. It is shown that the upper and lower bounds are obtained by replacing the parameters of the signal quantum state with the renormalized parameters including the thermal noise effects in the accessible information and the minimum value of the Bayes cost in quantum detection processes in thr absence of thermal noise. Analytic expressions of the upper and lower bounds are given for several quantum state signals.