Security Bounds for Quantum Cryptography with Finite Resources

TL;DR

This paper analyzes the security of quantum key distribution protocols when only a finite amount of communication is exchanged, providing practical bounds and simplifying implementation assumptions for real-world quantum cryptography.

Contribution

It introduces new security bounds for finite-resource QKD, shows symmetrization steps can be omitted, and incorporates two-way reconciliation in the security analysis.

Findings

Finite-resource security bounds for device-independent QKD.

Symmetrization steps can be omitted in practical implementations.

Two-way reconciliation protocols can be included in security proofs.

Abstract

A practical quantum key distribution (QKD) protocol necessarily runs in finite time and, hence, only a finite amount of communication is exchanged. This is in contrast to most of the standard results on the security of QKD, which only hold in the limit where the number of transmitted signals approaches infinity. Here, we analyze the security of QKD under the realistic assumption that the amount of communication is finite. At the level of the general formalism, we present new results that help simplifying the actual implementation of QKD protocols: in particular, we show that symmetrization steps, which are required by certain security proofs (e.g., proofs based on de Finetti's representation theorem), can be omitted in practical implementations. Also, we demonstrate how two-way reconciliation protocols can be taken into account in the security analysis. At the level of numerical estimates, we present the bounds with finite resources for ``device-independent security'' against collective attacks.