Min-entropy as a resource for one-shot private state transfer, quantum masking, and state transition

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 or 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 a quantum one-time pad. Then, through the equivalence of quantum secret sharing–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 half the size of the quantum state it can catalytically dephase. This gives a necessary and sufficient condition for catalysts for state transition processes.