Quantum consensus dynamics by entangling Maxwell demon

We introduce a Maxwell demon which generates many-body entanglement robustly against bit-flip noises, allowing us to obtain quantum advantage. Adopting the protocol of the voter model used for opinion dynamics approaching consensus, the demon randomly selects a qubit pair and performs a quantum feedback control, in continuous repetitions. We derive upper bounds for the entropy reduction and the work extraction rates by the demon's operation. These bounds are determined by a competition between the quantum-classical mutual information acquired by the demon and the absolute irreversibility of the feedback control. Our finding of the upper bounds corresponds to a reformulation of the second law of thermodynamics under a class of Maxwell demon which generates many-body entanglement in a working substance. This suggests that a general condition for the operation of a successful entangling demon, one for which many-body entanglement stabilization and work extraction are possible, is that the information gain is larger than the absolute irreversibility.