General immunity and superadditivity of two-way Gaussian quantum cryptography

TL;DR

This paper proves that two-way Gaussian quantum key distribution protocols are inherently more secure than one-way protocols, demonstrating superadditivity of security thresholds and immunity to advanced eavesdropping strategies in the asymptotic limit.

Contribution

The authors establish the superadditivity of two-way Gaussian QKD security thresholds and demonstrate immunity to coherent attacks, introducing a novel on/off switching technique for enhanced security.

Findings

Two-way Gaussian protocols have higher security thresholds than one-way protocols.

The superadditivity of security thresholds is achieved through random on/off switching.

The security enhancement holds against collective and coherent attacks.

Abstract

We consider two-way continuous-variable quantum key distribution, studying its security against general eavesdropping strategies. Assuming the asymptotic limit of many signals exchanged, we prove that two-way Gaussian protocols are immune to coherent attacks. More precisely we show the general superadditivity of the two-way security thresholds, which are proven to be higher than the corresponding one-way counterparts in all cases. We perform the security analysis first reducing the general eavesdropping to a two-mode coherent Gaussian attack, and then showing that the superadditivity is achieved by exploiting the random on/off switching of the two-way quantum communication. This allows the parties to choose the appropriate communication instances to prepare the key, accordingly to the tomography of the quantum channel. The random opening and closing of the circuit represents, in fact, an additional degree of freedom allowing the parties to convert, a posteriori, the two-mode correlations of the eavesdropping into noise. The eavesdropper is assumed to have no access to the on/off switching and, indeed, cannot adapt her attack. We explicitly prove that this mechanism enhances the security performance, no matter if the eavesdropper performs collective or coherent attacks.