Second law of information thermodynamics with entanglement transfer.

We present an inequality which holds in the thermodynamical processes with measurement and feedback controls and uses only the Helmholtz free energy and the entanglement of formation: W(ext)≤-ΔF-k(B)TΔE(F). The quantity -ΔE(F), which is positive, expresses the amount of entanglement transfer from system S to probe P through the interaction U(SP) during the measurement. It is easier to achieve the upper bound in this inequality than in the Sagawa-Ueda inequality [Phys. Rev. Lett. 100, 080403 (2008)]. Our inequality has clear physical meaning: in the above thermodynamical processes, the work which we can extract from the thermodynamic system is greater than the upper bound in the conventional thermodynamics by the amount of the entanglement extracted by the measurement.