Two-way quantum cryptography at different wavelengths

We study the security of two-way quantum cryptography at different wavelengths of the electromagnetic spectrum, from the optical down to the microwave range. In particular, we consider a two-way quantum communication protocol where Gaussian-modulated thermal states are subject to random Gaussian displacements and finally homodyned. We show how its security threshold (in reverse reconciliation) is extremely robust with respect to the preparation noise and able to outperform the security thresholds of one-way protocols at any wavelength. As a result, improved security distances are now accessible for implementing quantum key distribution in the very challenging regime of infrared frequencies.