Evaluating the Eavesdropper Entropy via Bloch-Messiah Decomposition

TL;DR

This paper uses Bloch-Messiah decomposition to analyze eavesdropper entropy in continuous variable QKD, providing tighter bounds on security by simplifying the attack model into basic optical operations.

Contribution

It introduces a novel application of Bloch-Messiah decomposition to derive tighter upper bounds on eavesdropper entropy in discrete modulated CVQKD protocols.

Findings

Tighter upper bounds on eavesdropper entropy achieved.

Decomposition simplifies the attack analysis into basic optical components.

Bounds are justified by Gaussian extremality properties.

Abstract

We explore the Bloch-Messiah decomposition of Gaussian unitary to analyze the Entangling Cloner Attack performed by an eavesdropper on a discrete modulated continuous variable QKD scenario. Such a decomposition allows to replace the nonlinear unitary resulting from eavesdropping and tracing out Bob's mode into an architecture of single-mode operations (squeezers, phase shifters and displacements) and a two-mode beam splitter. Based on such architecture we were able to get tighter upper bounds to the eavesdropper entropy for a discrete modulated CVQKD scheme. The new bounds are justified from the Gaussian extremality property valid for entangled-based equivalent protocols.