Entangled thermal mixed states for multi-qubit systems

We derive the entangled thermal mixed states by using the formalism of phase states for a finite-dimensional algebra of a multi-qubit system in contact with an independent thermal environment of absolute temperature T. Thermal entangled states describing the multi-qubit system in equilibrium with the thermal bath are a special kind of mixed states that exhibit genuine multipartite correlation. We define the unitary phase operators for a multipartite system of non-interacting qubits. Entangled density matrices are derived for qubits interacting via an Hermitian Hamiltonian of Heisenberg type (H). By assuming that the noisy interaction of the entangled qubit ensemble with the bath is governed by a local Hamiltonian (H-0), we show that the entangled phase states can be decohered. When the multi-qubits entangled system reaches the equilibrium with the thermal bath, the decohered mixed states are identified with entangled thermal states. The thermal mixed states for bipartite and multipartite systems are explicitly expressed and their bipartite entanglement properties are investigated.