Security Proof for Variable-Length Quantum Key Distribution

Abstract

We present a security proof for variable-length QKD in the Renner framework against IID collective attacks. Our proof can be lifted to coherent attacks using the postselection technique. Our first main result is a theorem to convert a series of security proofs for fixed-length protocols satisfying certain conditions to a security proof for a variable-length protocol. This conversion requires no new calculations, does not require any changes to the final key lengths or the amount of error-correction information, and at most doubles the security parameter. Our second main result is the description and security proof of a more general class of variable-length QKD protocols, which does not require characterizing the honest behaviour of the channel connecting the users before the execution of the QKD protocol. Instead, these protocols adaptively determine the length of the final key, and the amount of information to be used for error-correction, based upon the observations made during the protocol. We apply these results to the qubit BB84 protocol, and show that variable-length implementations lead to higher expected key rates than the fixed-length implementations.

arXiv commentMinor updates to match published version

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Cited by in corpus (12)

• Postselection technique for optical Quantum Key Distribution with improved de Finetti reductions
• Experimental composable key distribution using discrete-modulated continuous variable quantum cryptography
• Finite-size analysis of prepare-and-measure and decoy-state QKD via entropy accumulation
• Generalized Numerical Framework for Improved Finite-Sized Key Rates with Rényi Entropy
• A consolidated and accessible security proof for finite-size decoy-state quantum key distribution
• Generalized Rényi entropy accumulation theorem and generalized quantum probability estimation
• Phase error rate estimation in QKD with imperfect detectors
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• High-dimensional quantum communication with scalable photonic entanglement in time and frequency