Thermodynamic work gain from entanglement

We show that entanglement can be utilized to extract the thermodynamic work beyond classical correlation via feedback control based on measurement on part of a composite system. The net work gain due to entanglement is determined by the change in the mutual information content between the subsystems that is accessible to the memory.

Figure 1

Schematic illustration of our setup. We perform a measurement on subsystem $A$ of an initially entangled composite system $AB$ and obtain an outcome $k$. We then perform a feedback control on each subsystem via a local unitary operation that depends on $k$. The thermodynamic cycle is completed with the initialization or erasure of the memory.

Figure 2

Entropy transfer in the protocol: (a) $A$ and $B$ are initially entangled, where the negative entropy is described by the quantum mutual information $-I({\rho }_{\mathrm{i}}^A:{\rho }_{\mathrm{i}}^B)$. We can decrease the entropy of $A$ and $B$ up to $I({\rho }_{\mathrm{i}}^A:{\rho }_{\mathrm{i}}^B)$ by performing an appropriate unitary transformation on the entire system. (b) Measurement on $A$ and entropy transfer from the system to $M$. The information gain of subsystem $A$ is given by $-I({\rho }_{\mathrm{i}}^A:X^M)$ and that of subsystem $B$ by $-I({\rho }_{\mathrm{i}}^B:X^M)$, whereas the memory generates a positive entropy $I({\rho }_{\mathrm{i}}^{AB}:X^M)$. (c) Feedback control performed on both $A$ and $B$ produces negative entropies $-I({\rho }_{\mathrm{i}}^A:X^M)$ and $-I({\rho }_{\mathrm{i}}^B:X^M)$, which arise from the initial correlation $-I({\rho }_{\mathrm{i}}^A:{\rho }_{\mathrm{i}}^B)$ and information gain $-I({\rho }_{\mathrm{i}}^{AB}:X^M)$. Consequently, the total entropy of $A$ and $B$ decreases, and work can be extracted from them. The correlation $I({\rho }_{\mathrm{i}}^A:{\rho }_{\mathrm{i}}^B|X^M)$ between $A$ and $B$ remains nonvanishing, which, however, cannot be utilized unless $A$ and $B$ are brought together to perform an appropriate unitary transformation on the entire state.