  We give an operational meaning to the min-entropy of a quantum state as a
resource measure for various interconnected tasks. In particular, we show that
the min-entropy without smoothing measures the amount of quantum information
that can be hidden or encoded perfectly in the one-shot setting when the
quantum state is used as a randomness/correlation source. First, we show that
the min-entropy of entanglement of a pure bipartite state is the maximum number
of qubits privately transferable when the state is used as quantum one-time
pad. Then, through the equivalence of quantum secret sharing(QSS)-like
protocols, it is also shown that the min-entropy of a quantum state is the
maximum number of qubits that can be masked when the state is used as a
randomness source for a quantum masking process. Consequently we show that the
min-entropy of a quantum state is the half of the size of quantum state it can
catalytically dephase.This gives a necessary and sufficient condition for
catalysts for state transition processes.
