Convex-roof entanglement measures of density matrices block diagonal in disjoint subspaces for the study of thermal states

We provide a proof that entanglement of any density matrix which is block diagonal in subspaces are disjoint terms the Hilbert space one two potentially entangled subsystems can simply be calculated as weighted average present within each block. This especially useful for thermal-equilibrium states always inherit symmetries Hamiltonian, since block-diagonal Hamiltonians common, interactions involve only single degree freedom greater system. exemplify our method on simple showing diversity possible temperature dependences Gibbs state emerge different parameter ranges.