One-Shot Min-Entropy Calculation And Its Application To Quantum Cryptography

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.