  We introduce a Maxwell demon which generates many-body entanglement robustly
against bit-flip noises, which allows 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 of the
entropy reduction and the work extraction rates by demon's operation, which 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.
