Multi-mode states in decoy-based quantum key distribution protocols

TL;DR

This paper investigates the impact of multi-mode quantum states in decoy-based QKD protocols, revealing how multi-mode effects can both threaten security and enhance key rates, depending on the mode structure.

Contribution

It introduces new bounds for single-photon transmission and error rates in multi-mode states and analyzes their effects on PDC-based QKD security.

Findings

Multi-mode structure introduces a new attack reducing key rate.

Multiple modes can shift photon distribution from thermal to Poissonian, increasing key rate.

The analysis highlights the importance of accurate multi-mode modeling in QKD security.

Abstract

Every security analysis of quantum key distribution (QKD) relies on a faithful modeling of the employed quantum states. Many photon sources, like for instance a parametric down conversion (PDC) source, require a multi-mode description, but are usually only considered in a single-mode representation. In general, the important claim in decoy-based QKD protocols for indistinguishability between signal and decoy states does not hold for all sources. We derive new bounds on the single photon transmission probability and error rate for multi-mode states, and apply these bounds to the output state of a PDC source. We observe two opposing effects on the secure key rate. First, the multi-mode structure of the state gives rise to a new attack that decreases the key rate. Second, more contributing modes change the photon number distribution from a thermal towards a Poissonian distribution, which increases the key rate.