Minimal energy cost of thermodynamic information processes only with entanglement transfer

We present the minimal energy costs for the measurement and the information erase, using only the Helmholtz free energy and the entanglement of formation. The entanglement of formation appears in the form of difference which indicates the amount of entanglement transfer on the memory during the processes; the cost of the measurement is given by the entanglement gain, whereas the cost of the information erase is given by the loss of available entanglement. Putting together the present Letter and Rev. E 88, 042143 (2013), we can describe the violation and the restoration of the second law only in terms of the entanglement of formation; both of the excess of extracted work from thermodynamics with information process over the conventional second law and the total cost of the information process are given by the entanglement of formation, and the former is less than or equal to the latter.