Entanglement which originates from a pair of non-interactingqubits by means of entanglement swapping is discussed when dephasing mechanisms are present. Then, the exact reduced dynamics can be evaluated for two pairs of independent qubitswhich each are coupled to their own bosonic environment.Each of two pairs of qubits is initially maximally entangled.The conditions for the entanglement survival at asymptoticlong times in terms of environment spectral properties are elab-orated. It is shown that these conditions hold true also forthe inter—pair entanglement stemming. Entanglement swap-ping can effectively been controlled by a proper choice of ini-tial state of the finite environment. Two non-interacting pairs of qubits, {S_1,S_2} and {3, 4},are in a separable state, wherein each pair of qubits is max-imally entangled. The Bell state measurement (BSM) on thepair {S_2,S_4} creates the entanglement of qubits S_1andS_3. The qubits are coupled to their own environments R_i, i=1,... 4.
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