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Physical Review A

Continuous-variable quantum key distribution with noisy coherent states

Radim Filip

Published Feb 11, 2008• 97 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.77.022310

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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.
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 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.
Security of a continuous-variable quantum key distribution protocol based on noisy coherent states and channel is analysed. Assuming that the noise of coherent states is induced by Fred, a neutral party relative to others, we prove that the prepare-and-measurement scheme (P&M) and entanglement-based scheme (E-B) are equivalent. Then, we show that this protocol is secure against Gaussian collective attacks even if the channel is lossy and noisy, and, further, a lower bound to the secure key rate is derived.
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.
In this paper, we present three continuous variable quantum key distribution protocols (named two-, four-, and eight-state protocols) based on the discrete modulation of phase coherent states. We investigate the security of these protocols against the collective eavesdropping attacks and show their performance in a realistic setup by taking into consideration the realistic lossy noisy quantum channels, and the imperfection of detection. We show that the use of phase coherent states gives better performance in terms of noise tolerance, key rate, and achievable distance than that of common linear coherent states.