  Work extraction is one of the most central processes in quantum
thermodynamics. However, the prior analysis of optimal extractable work has
been restricted to a limited operational scenario where complete information
about the initial state is given. Here, we introduce a general framework of
black box work extraction, which addresses the inaccessibility of information
on the initial state. We show that the optimal extractable work in the black
box setting is completely characterized by the performance of a composite
hypothesis testing task, a fundamental problem in information theory.We employ
this general relation to reduce the asymptotic black box work extraction to the
quantum Stein's lemma in composite hypothesis testing, allowing us to provide
their exact characterization in terms of the Helmholtz free energy. We also
show a new quantum Stein's lemma motivated in this physical setting, where a
composite hypothesis contains a certain correlation. Our work exhibits the
importance of information about the initial state and gives a new
interpretation of the quantities in the composite quantum hypothesis testing,
encouraging the interplay between the physical settings and the information
theory.
