  The information of a quantum system acquired by a Maxwell demon can be used
for either work extraction or entanglement preparation. We study these two
tasks by using a thermal qubit, in which a demon obtains her information from
measurements on the environment of the qubit. The allowed entanglement, between
the qubit and an auxiliary system, is enhanced by the information. And, the
increment is find to be equivalent to the extractable work. The Maxwell demon
is called to be quantum by Beyer \textit{et al.} [Phys. Rev. Lett 123, 250606
(2019) ] if there is quantum steering from the environment to the qubit. In
this case, the postmeasured states of the qubit, after the measurements on its
environment, cannot be simulated by an objective local statistical ensemble. We
present a upper bound of extractable work, and equivalently of the allowed
entanglement, for unsteerable demons, considering two measurements inducing two
orthogonal changes of the Bloch vector of the qubit.
