  Feedback control and erasure protocols have often been considered as a model
to embody Maxwell's Demon paradox and to study the interplay between
thermodynamics and information processing. Such studies have led to the
conclusion, now widely accepted in the community, that Maxwell's Demon and the
second law of thermodynamics can peacefully coexist because any gain provided
by the demon must be offset by the cost of performing measurement and resetting
the demon's memory to its initial state. Statements of this kind are
collectively referred to as second laws of information thermodynamics and have
recently been extended to include quantum theoretical scenarios. However,
previous studies in this direction have made several assumptions, in particular
about the feedback process and the measurement performed on the demon's memory,
and thus arrived at statements that are not universally applicable and whose
range of validity is not clear. In this work, we fill this gap by precisely
characterizing the full range of quantum feedback control and erasure protocols
that are overall consistent with the second law of thermodynamics. This leads
us to conclude that the second law of information thermodynamics is indeed
universal: it must hold for any quantum feedback control and erasure protocol,
regardless of the measurement process involved, as long as the protocol is
overall compatible with thermodynamics. Our comprehensive analysis not only
encompasses new scenarios but also retrieves previous ones, doing so with fewer
assumptions. This simplification contributes to a clearer understanding of the
theory. Additionally, our work identifies the Groenewold--Ozawa information
gain as the correct information measure characterizing the work extractable by
feedback control.
