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Research in Optical Sciences

Two-way quantum cryptography with continuous variables: unconditional security and performances at different wavelengths

Carlo Ottaviani, Stefano Pirandola

Published Jan 1, 2014• 0 citations
Publisher

Abstract

In first place we analysed the security of two-way QKD against coherent attacks achieving unconditional security in all encoding/decoding configurations. In second place we studied the security, at different wavelengths, of two-way thermal QKD finding a robust threshold in reverse reconciliation, improving the security distances for continuous variable quantum cryptography in the infrared.

DOI
10.1364/qim.2014.qw3a.3

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In first place we analysed the security of two-way QKD against coherent attacks achieving unconditional security in all encoding/decoding configurations. In second place we studied the security, at different wavelengths, of two-way thermal QKD finding a robust threshold in reverse reconciliation, improving the security distances for continuous variable quantum cryptography in the infrared.
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.
This thesis deals with a detailed study of the unconditional security of Continuous-Variable (CV) Quantum Key Distribution (QKD). We consider general communication architectures based on both point-to-point and end-to-end principle. For the first case we develop an extensive analysis of the unconditional security of both one-way and two-way protocol under several eavesdropping conditions. We describe an effective post-processing strategy, to apply to one-way communications, that allows to neutralise general coherent attacks. This result motivates us to formulate the conjecture that the "de Finettization" of the classical data, typically adopted in the asymptotic limit of many signals exchanged in order to reduce the attacks from a general coherent to a collective one, may not be necessary for Gaussian one-way communication. For what it concerns two-way protocols we show that after the reduction of the general attack using the de Finetti symmetrization, two-mode coherent attacks are the optimal eavesdropping. Our cryptanalysis shows that the parties can exploit a strategy, in combination with the results obtained on the security of one-way protocols against two-mode coherent attacks. In fact we prove explicitly that two-way communication with Gaussian continuous variables is immune to general coherent attacks. This is possible exploiting the random opening and closing of the circuit by Alice (ON/OFF switching), in the limit of many uses of the channel. We then conclude that collective attacks represent, strictly, the best strategy available to Eve. We have then studied the general security of one-way protocol considering not just lossy channel, but extending the cryptanalysis to all physically allowed canonical forms attacks. Finally we extended the study of thermal CV-QKD to two-way communication at different frequencies, in the framework of optimal collective attacks. In the last part of this thesis we focused on CV-QKD considering a modern end-to-end configuration. We then extend CV quantum cryptography to a network configuration. We develop a detailed cryptoanalysis of a communication scheme based on an untrusted relay, assisting the parties during the preparation of the secret key. We find the optimal eavesdropping and prove, both theoretically and experimentally, the feasibility of high-rate CV-QKD over metropolitan distances with of-the-shelves devices.
Recently, we have shown the advantages of two-way quantum communications in continuous variable quantum cryptography. Thanks to this new approach, two honest users can achieve a non-trivial security enhancement as long as the Gaussian interactions of an eavesdropper are independent and identical. In this work, we consider asymmetric strategies where the Gaussian interactions can be different and classically correlated. For several attacks of this kind, we prove that the enhancement of security still holds when the two-way protocols are used in direct reconciliation.
We extend the asymptotic security of continuous variable quantum key distribution using one-way and two-way quantum communication to a multi-way setting: Quantum signals travel many times between the parties before the final detection. We assume that the encoded signals are Gaussian-modulated coherent states that travel each time through the same Gaussian channel characterized by loss and thermal noise. We then quantify the reverse-reconciliation performance of the protocol presenting results for even or odd numbers of signal exchange.