Minimum-error discrimination of thermal states

We study several variations of the question minimum-error discrimination thermal states. Besides providing optimal values for probability error, we also characterize measurements. For case a fixed Hamiltonian, show that general problem measurement is in energy basis Hamiltonian. identify critical temperature, determining whether given temperature best distinguishable from state very high or low temperatures. Further, investigate decision above below some threshold value temperature. Also, this case, basis. This no longer once states to be discriminated have different Hamiltonians. analyze specific situation when but Hamiltonians are different. considered independent and strength interaction.