Finite-key security analysis of the decoy-state BB84 QKD with passive measurement

TL;DR

This paper provides an analytical finite-key security proof for the decoy-state BB84 quantum key distribution protocol with passive measurement, demonstrating that passive basis choice maintains comparable key rates to active methods.

Contribution

It introduces the first simple analytical finite-key security proof for decoy-state BB84 with passive basis choice, including a closed-form secret-key rate formula.

Findings

Passive and active measurement implementations have nearly identical key rates.

Passive measurement does not reduce key-generation efficiency in practical QKD.

The security proof is directly applicable using experimentally accessible parameters.

Abstract

The decoy-state Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol is widely regarded as the de facto standard for practical implementations. On the receiver side, passive basis choice is attractive because it significantly reduces the need for random number generators and eliminates the need for optical modulators. Despite these advantages, a finite-key analytical security proof for the decoy-state BB84 protocol, where the basis is chosen passively with a biased probability, has been lacking. In this work, we present a simple analytical finite-key security proof for this setting, yielding a closed-form secret-key rate formula that can be directly evaluated using experimentally accessible parameters. Numerical simulations show that the key rates of passiveand active-measurement implementations are nearly identical, indicating that passive measurement does not compromise key-generation efficiency in practical QKD systems.