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

TL;DR

This paper introduces a one-shot lower bound method for calculating min-entropy in classical-quantum states, enhancing quantum cryptography security analysis and applicable to various protocols.

Contribution

It develops a practical technique for min-entropy bounds applicable to finite and infinite-dimensional states, improving quantum cryptography security proofs.

Findings

Provides a tight finite-data analysis for BB84 QKD

Achieves the best finite-key bound for a device-independent QKD variant

Secures a source-independent continuous-variable quantum random number generator

Abstract

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 three situations. First, it offers an alternative tight finite-data analysis for the BB84 quantum key distribution scheme. Second, it gives the best finite-key bound known to date for a variant of device independent quantum key distribution protocol. Third, it provides a security proof for a novel source-independent continuous-variable quantum random number generation protocol. These results show the effectiveness and wide applicability of our approach.