  The so-called quasi-Bell entangled coherent states in a thermal environment
are studied. In the analysis, we assume thermal noise affects only one of the
two modes of each state. First the matrix representation of the density
operators of the quasi-Bell entangled coherent states in a thermal environment
is derived. Secondly we investigate the entanglement property of one of the
quasi-Bell entangled coherent states with thermal noise. At that time a lower
bound of the entanglement of formation for the state is computed. Thirdly the
minimax discrimination problem for two cases of the binary set of the
quasi-Bell entangled coherent states with thermal noise is considered, and the
error probabilities of the minimax discrimination for the two cases are
computed with the help of Helstrom's algorithm for finding the Bayes optimal
error probability of binary states.
