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NATO science for peace and security series. D, Information and communication security

Trusted noise in continuous-variable quantum key distribution

Vladyslav C. Usenko, Radim Filip

Published Jan 1, 2010• 0 citations
Publisher

Abstract

We address the problem of the security of the continuous variable quantum key distribution with the coherent states in the presence of a trusted noise of different origins, e.g. preparation noise at the sender side and the detection noise at the remote receiver side. We show the essential difference between the impact of these types of noise under conditions of lossy quantum channel, available to an eavesdropper. While detection noise reduces the key rate without breaking the security, the preparation noise is destructive for the secure transmission. At the same time we show that by the state purification we can compensate for the destructive effect of the preparation noise, so that upon optimal purification its impact becomes similar to that of the detection noise. The effect is persistent also upon realistic error correction.

DOI
10.3233/978-1-60750-547-1-99

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We address the problem of the security of the continuous variable quantum key distribution with the coherent states in the presence of a trusted noise of different origins, e.g. preparation noise at the sender side and the detection noise at the remote receiver side. We show the essential difference between the impact of these types of noise under conditions of lossy quantum channel, available to an eavesdropper. While detection noise reduces the key rate without breaking the security, the preparation noise is destructive for the secure transmission. At the same time we show that by the state purification we can compensate for the destructive effect of the preparation noise, so that upon optimal purification its impact becomes similar to that of the detection noise. The effect is persistent also upon realistic error correction.
We address security of the quantum key distribution scheme based on the noisy modulation of coherent states and investigate how it is robust against noise in the modulation regardless of the particular technical implementation. As the trusted preparation noise is shown to be security breaking even for purely lossy channels, we reveal the essential difference between two types of trusted noise, namely sender-side preparation noise and receiver-side detection noise, the latter being security preserving. We consider the method of sender-side state purification to compensate the preparation noise and show its applicability in the realistic conditions of channel loss, untrusted channel excess noise, and trusted detection noise. We show that purification makes the scheme robust to the preparation noise (i.e., even the arbitrary noisy coherent states can in principle be used for the purpose of quantum key distribution). We also take into account the effect of realistic reconciliation and show that the purification method is still efficient in this case up to a limited value of preparation noise.
We address the role of the phase-insensitive trusted preparation and detection noise in the security of a continuous-variable quantum key distribution, considering the Gaussian protocols on the basis of coherent and squeezed states and studying them in the conditions of Gaussian lossy and noisy channels. The influence of such a noise on the security of Gaussian quantum cryptography can be crucial, even despite the fact that a noise is trusted, due to a strongly nonlinear behavior of the quantum entropies involved in the security analysis. We recapitulate the known effect of the preparation noise in both direct and reverse-reconciliation protocols, as well as the detection noise in the reverse-reconciliation scenario. As a new result, we show the negative role of the trusted detection noise in the direct-reconciliation scheme. We also describe the role of the trusted preparation or detection noise added at the reference side of the protocols in improving the robustness of the protocols to the channel noise, confirming the positive effect for the coherent-state reverse-reconciliation protocol. Finally, we address the combined effect of trusted noise added both in the source and the detector.
The role of the side channels in the continuous-variable quantum key distribution is studied. It is shown how the information leakage through a side channel from the trusted sender station increases the vulnerability of the protocols to the eavesdropping in the main quantum communication channel. Moreover, the untrusted noise infusion by an eavesdropper on the trusted receiving side breaks the security even for a purely attenuating main quantum channel. As a method to compensate for the effect of the side-channel leakage on the sender side, we suggest several types of manipulations on the side-channel input. It is shown that by applying the modulated coherent light on the input of the side channel that is optimally correlated to the modulation on the main signal and optionally introducing additional squeezing in the case of the squeezed-state protocol, the negative influence of the lossy side channel on the sender side can be completely removed. For the trusted receiving side, the method of optimal monitoring of the residual noise from the side-channel noise infusion is suggested and shown to be able to completely eliminate the presence of the noisy side channel. We therefore prove that the side-channel effects can be completely removed using feasible operations if the trusted parties access the respective parts of the side channels.
We address the applicability of the continuous-variables quantum key distribution in the realistic conditions of noisy preparation, channel loss and detection noise and investigate the possibility to increase its tolerance to the state preparation noise. The two types of preparation noise, either phase-sensitive or phase-insensitive excess noise, are considered in the assumption of optimal attacks performed by an eavesdropper within the setup based on the entangled source and either homodyne or heterodyne measurements. We show that preparation noise is destructive for the secure channel upon even low noise variances in the conditions of channel loss, while detection noise just decreases the key rate. We propose the method of sender-side attenuation to suppress the preparation noise in the entanglements-based scheme and show that it enables the secure key transmission upon arbitrary high preparation noise of both types and any pure channel loss against both individual and collective attacks.
We address side-channel leakage in a trusted preparation station of continuous-variable quantum key distribution with coherent and squeezed states. We consider two different scenarios: multimode Gaussian modulation, directly accessible to an eavesdropper, or side-channel loss of the signal states prior to the modulation stage. We show the negative impact of excessive modulation on both the coherent- and squeezed-state protocols. The impact is more pronounced for squeezed-state protocols and may require optimization of squeezing in the case of noisy quantum channels. Further, we demonstrate that the coherent-state protocol is immune to side-channel signal state leakage prior to modulation, while the squeezed-state protocol is vulnerable to such attacks, becoming more sensitive to the noise in the channel. In the general case of noisy quantum channels the signal squeezing can be optimized to provide best performance of the protocol in the presence of side-channel leakage prior to modulation. Our results demonstrate that leakage from the trusted source in continuous-variable quantum key distribution should not be underestimated and squeezing optimization is needed to overcome coherent state protocols.
An excess noise in coherent-state preparation can prevent secure key distribution through lossy channel. The feasible single-copy and multicopy linear optical methods are proposed to purify the prepared state. The single-copy method always sufficiently reduces the excess noise to obtain the key secure against both the individual and collective attacks even through any lossy channel. To increase the secure key rate, two feasible applications of the multicopy linear optical purification are proposed. As a result, maximal secure key rate achievable through a given lossy channel can be approached.