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arXiv:1309.7973 · Physical Review A

Two-way quantum cryptography at different wavelengths

Christian Weedbrook, Carlo Ottaviani, Stefano Pirandola

Published Jan 10, 2014• 71 citations
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Abstract

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.

DOI
10.1103/physreva.89.012309

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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.
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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.
We study the impact of finite-size effects on the security of thermal one-way quantum cryptography. Our approach considers coherent and/or squeezed states at the preparation stage, on the top of which the sender adds trusted thermal noise. We compute the key rate incorporating finite-size effects, and we obtain the security threshold at different frequencies. As expected, finite-size effects deteriorate the performance of thermal quantum cryptography. Our analysis is useful to quantify the impact of this degradation on relevant parameters like tolerable attenuation and transmission frequencies at which one can achieve security.