Maxwell's demons in multipartite quantum correlated systems

We investigate the extraction of thermodynamic work by a Maxwell's demon in a multipartite quantum correlated system. We begin by adopting the standard model of a Maxwell's demon as a Turing machine, either in a classical or quantum setup depending on its ability to implement classical or quantum conditional dynamics. Then, for an $n$-partite system $(A_1,A_2,\cdots ,A_n)$, we introduce a protocol of work extraction that bounds the advantage of the quantum demon over its classical counterpart through the amount of multipartite quantum correlation present in the system, as measured by a thermal version of the global quantum discord. This result is illustrated for an arbitrary $n$-partite pure state of qubits with Schmidt decomposition, where it is shown that the thermal global quantum discord exactly quantifies the quantum advantage. Moreover, we also consider the work extraction via mixed multipartite states, where examples of tight upper bounds can be obtained.

Figure 1

Protocol for sequential work extraction in a multipartite scenario, where subsystem $A_i$ is taken as the apparatus at intermediate step $i$. For subsystems $A_j$, with $j<i$, the classical demon applies a nonselective measurement to optimize the local extracted work from subsystem $A_i$.

Figure 2

Quantum circuit for work extraction in the case of an $n$-qubit pure state $|{\psi }_{A_1\cdots A_n}^{\left(i\right)}\rangle =\alpha |0\cdots 0\rangle +\beta |1\cdots 1\rangle$. The initial state is $|{\psi }_{A_1\cdots A_n}^{\left(i\right)}{\rangle \otimes |0\rangle }_D$. The quantum demon is able to purify the individual states of subsystems $A_1,\cdots ,A_n$ while resetting its memory to the ready-to-measure state ${|0\rangle }_D$.

Figure 3

Multipartite MID (black circles), thermal GQD (red squares), and the total quantum advantage $\Delta W_t$ for work extraction (green diamonds) as a function of $\lambda$ for the $W$-GHZ state. Note that the thermal GQD is an upper bound for $\Delta W_t$, while MID is a global upper bound for the other quantities.