The Min-entropy as a Resource for One-Shot Private State Transfer, Quantum Masking and State Transition

Abstract: 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.