Heat Engine Driven by Purely Quantum Information

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.

Figure 1

The schematic picture showing the setup considered here. The system is attached to the reservoir, and is measured and controlled by the memory consisting of $A$ and $B$. (See the text for the details.)

Figure 2

The SZE containing a molecule with two internal states $A$ and $B$ prepared in the Bell’s state. (a) A wall, depicted as a vertical gray bar, is inserted to split the box into two parts. The molecule is represented by the dotted circles so as to indicate that at this stage we do not know in which box the molecule is. (b) By applying the unitary operator we have the state given by Eq. (18). The SPWs are then inserted so that $W_{|\downarrow ⟩}$ is in the left and $W_{|\uparrow ⟩}$ in the right of the wall, and, consequently, the wall is removed. (c) A load is attached to each SPW to extract work via an isothermal expansion at a constant temperature $T$.