The key question of this Letter is whether work can be extracted from a heat engine by using purely quantum mechanical information. If the answer is yes, what is its mathematical formula? First, by using a bipartite memory we show that the work extractable from a heat engine is bounded not only by the free energy change and the sum of the entropy change of an individual memory but also by the change of quantum mutual information contained inside the memory. We then find that the engine can be driven by purely quantum information, expressed as the so-called quantum discord, forming a part of the quantum mutual information. To confirm it, as a physical example we present the Szilard engine containing a diatomic molecule with a semipermeable wall.

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Kim et al. Reply: In discussing our Letter [1],it is important (I) to understand the phrase "confined-to-propagating transition of LO phonons" properly and (2) to realize how the experimental hot phonon occupation number can be sensitive to such a transition.When we suggest that LO phonons are propagating and not confined, we do not intend to imply directly that there is a significant probability of finding the GaAs LO phonons in the alloy barrier region. The eigenvector ratio

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