Continuous-variable quantum cryptography using two-way quantum communication

Abstract

Quantum cryptography has been recently extended to continuous variable systems, e.g., the bosonic modes of the electromagnetic field. In particular, several cryptographic protocols have been proposed and experimentally implemented using bosonic modes with Gaussian statistics. Such protocols have shown the possibility of reaching very high secret key rates, even in the presence of strong losses in the quantum communication channel. Despite this robustness to loss, their security can be affected by more general attacks where extra Gaussian noise is introduced by the eavesdropper. In this general scenario we show a "hardware solution" for enhancing the security thresholds of these protocols. This is possible by extending them to a two-way quantum communication where subsequent uses of the quantum channel are suitably combined. In the resulting two-way schemes, one of the honest parties assists the secret encoding of the other with the chance of a non-trivial superadditive enhancement of the security thresholds. Such results enable the extension of quantum cryptography to more complex quantum communications.In recent years, quantum information has entered the domain of continuous variable (CV) systems, i.e., quantum systems described by an infinite dimensional Hilbert space [1,2]. So far, the most studied CV systems are the bosonic modes, such as the optical modes of the electromagnetic field. In particular, the most important bosonic states are the ones with Gaussian statistics, thanks to their experimental accessibility and the relative simplicity of their mathematical description [3,4]. Accordingly, quantum key distribution (QKD) has been extended to this new framework [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21] and Gaussian cryptographic protocols using coherent states have been shown to exploit fully the potentialities of quantum optics [12,16]. These coherentstate protocols are robust with respect to the noise of the quantum channel, as long as such noise can be ascribed to pure losses [12,16]. By contrast, their security is strongly affected when channel losses are used to introduce a thermal environment, which is assumed to be controlled by a malicious eavesdropper [12,22]. In this Gaussian eavesdropping scenario, we present a method to enhance the security thresholds of the basic coherent-state protocols. This is achieved by extending them to two-way quantum communication protocols, where one of the honest parties (Bob) uses its quantum resources to assist the secret encoding of the other party (Alice). In particular, the enhancement of security is proven to be effective since the security thresholds are superadditive with respect to the double use of the quantum channel. Such a result is achieved when the Gaussian attack corresponds to a memoryless Gaussian channel. More generally, we also consider Gaussian channels with memory, therefore creating classical and/or quantum correlations between the paths of the two-way quantum communication. In order to overcome this kind of eavesdropping strategy, the tw...

Fundamental rate-loss tradeoff for optical quantum key distribution

“…We will also extend our upper bound to the more general scenario of QKD using a two-way quantum channel with unlimited public discussion, which was discussed recently in ref. 15. Finally, we will compare our upper bound and the best-known lower bound to the rate achievable by the BB84 and the CV-GG02 protocols under best-case operating conditions as well as compare with the performance of these protocols under realistic operating conditions.…”

Quantum Cryptography Approaching the Classical Limit

“…03.67.Dd, 03.67.Hk, 89.70.Cf Introduction -Quantum key distribution (QKD) using continuous variables (CV) [1,2] allows two people, Alice and Bob, to generate a secure key which can be used to encrypt messages. CV-QKD protocols using Gaussian modulation [3][4][5][6][7][8], initially begin with Alice preparing a number of randomly displaced pure coherent states and sending them over an insecure quantum channel to Bob. Generally, it is assumed that Alice's states must be pure quantum states to a good approximation otherwise her ability to perform QKD will rapidly become compromised.…”

“…CV-QKD protocols using Gaussian modulation [3][4][5][6][7][8], initially begin with Alice preparing a number of randomly displaced pure coherent states and sending them over an insecure quantum channel to Bob. Generally, it is assumed that Alice's states must be pure quantum states to a good approximation otherwise her ability to perform QKD will rapidly become compromised.…”

“…Future analysis will look at improving the region where infrared and microwave CV-QKD is secure. For example, in [6] they showed that the security thresholds for direct reconciliation could be improved (and in fact beat the 3 dB loss limit) if two-way quantum communication was used. Furthermore, post-selection [7] could also be used to investigate a possible way to combat the high preparation noise.…”

Finite Key Size Analysis of Two-Way Quantum Cryptography

“…Conversely, when the errors in EM is higher, it is likely the case that LM05 may not perform better than BB84 except for possible very small error rates. We conclude saying that a finite key analysis would be enlightening also for two-way QKD in the framework of continuous variable [29].…”