Quasi-Bell entangled coherent states and its quantum discrimination problem in the presence of thermal noise

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.