  In quantum Shannon theory, various kinds of quantum entropies are used to
characterize the capacities of noisy physical systems. Among them, min-entropy
and its smooth version attract wide interest especially in the field of quantum
cryptography as they can be used to bound the information obtained by an
adversary. However, calculating the exact value or non-trivial bounds of
min-entropy are extremely difficult because the composite system dimension may
scale exponentially with the dimension of its subsystem. Here, we develop a
one-shot lower bound calculation technique for the min-entropy of a
classical-quantum state that is applicable to both finite and infinite
dimensional reduced quantum states. Moreover, we show our technique is of
practical interest in at least two situations. First, it gives an alternative
tight finite-data analysis for the well-known BB84 quantum key distribution
protocol. More importantly, it provides a security proof for a novel
source-independent continuous-variable quantum random number generation
protocol. These show the effectiveness and wide applicability of our approach.
