  We consider an extension of the conditional min- and max-entropies to
infinite-dimensional separable Hilbert spaces. We show that these satisfy
characterizing properties known from the finite-dimensional case, and retain
information-theoretic operational interpretations, e.g., the min-entropy as
maximum achievable quantum correlation, and the max-entropy as decoupling
accuracy. We furthermore generalize the smoothed versions of these entropies
and prove an infinite-dimensional quantum asymptotic equipartition property. To
facilitate these generalizations we show that the min- and max-entropy can be
expressed in terms of convergent sequences of finite-dimensional min- and
max-entropies, which provides a convenient technique to extend proofs from the
finite to the infinite-dimensional setting.

Quantum Physics