Security Assumptions in Dispersive-Optics QKD

Quantum key distribution (QKD) seeks to provide a method of generating cryptographically-secure keys between remote parties while guaranteeing unconditional security. Implementations of high-dimensional QKD using dispersive-optics (DO-QKD) have been proposed to allow for multiple secure bits to be transmitted per photon while remaining cost-effective and scalable using existing telecommunication technology [1]. In the recent literature, there have been a number of experimental realizations of DO-QKD systems [2-6], with security analysis based on the treatment in Ref. [1]. Here we demonstrate that in the case of finite dispersion, the model assumed for the eavesdropper's attack in Ref. [1] is non-optimal for the eavesdropper, which leads to a significant overestimation of the secure key rate between parties. We consider an alternative attack model that Alice and Bob find indistinguishable from the Ref. [1] model, as long as they are restricted to making the measurements typical in DO-QKD. We provide concrete examples where a significant gap exists between the Holevo information, and therefore the secret key rate, predicted by the two models. We further analyze the experiment in Ref. [2] as an example of a case where secure key is predicted according to the Ref. [1] model, but where in fact there is zero secure key rate when considering the full set of collective attacks that an eavesdropper may perform.