Steering Heat Engines: A Truly Quantum Maxwell Demon

We address the question of verifying the quantumness of thermal machines. A Szilárd engine is truly quantum if its work output cannot be described by a local hidden state model, i.e., an objective local statistical ensemble. Quantumness in this scenario is revealed by a steering-type inequality which bounds the classically extractable work. A quantum Maxwell demon can violate that inequality by exploiting quantum correlations between the work medium and the thermal environment. While for a classical Szilárd engine an objective description of the medium always exists, any such description can be ruled out by a steering task in a truly quantum case.

Figure 1

Work extraction. Bob has blue and red work extraction cells with locally thermal qubits. The reduced state ${\rho }_{\mathcal{S}}$ can be decomposed into statistical mixture of $|1⟩$ and $|0⟩$ or the two states given by the Bloch vectors ${\overrightarrow{r}}_{\pm }$. Different unitaries can be used to bring the states to the ground state extracting some work. The red cells can apply the ${\mathcal{U}}_z^1$ and the identity operation. Qubits in the blue cells can be manipulated by two unitaries ${\mathcal{U}}_x^{\pm }$. Bob gets the information which unitary he should use from Alice. After the coupling process the work storage is measured in its energy basis.

Figure 2

The plot shows by how much Alice can violate the classical work bound. For parameters in the region below the red line Bob can explain the extracted work with a local hidden state model.