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arXiv:1101.0871 · Physical Review A

Continuous-variable quantum key distribution with Gaussian source noise

Yujie Shen, Xiang Peng, Jian Cheng Yang, Hong Mei Guo

Published May 6, 2011• 48 citations
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Abstract

Source noise affects the security of continuous-variable quantum key distribution (CV QKD) and is difficult to analyze. We propose a model to characterize Gaussian source noise through introducing a neutral party (Fred) who induces the noise with a general unitary transformation. Without knowing Fred's exact state, we derive the security bounds for both reverse and direct reconciliations and show that the bound for reverse reconciliation is tight.

DOI
10.1103/physreva.83.052304

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Source noise affects the security of continuous-variable quantum key distribution (CV QKD) and is difficult to analyze. We propose a model to characterize Gaussian source noise through introducing a neutral party (Fred) who induces the noise with a general unitary transformation. Without knowing Fred's exact state, we derive the security bounds for both reverse and direct reconciliations and show that the bound for reverse reconciliation is tight.
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.
Security of continuous-variable quantum key distribution with four-state protocol based on discrete modulation of noisy coherent states is analyzed. Combing discrete modulation and reverse reconciliation, this protocol can be used for long distance cryptography. There is a small difference between the state Alice sends in the discrete modulation protocol and the Gaussian modulation protocol, and it can be treated as excess noise and loss in the channel. As Alice cannot do a precise modulation, she will induce noise to the coherent state. We look this noise as the source noise and derive a lower bound to the secure key rate assuming the eavesdropper cannot benefit from the noise in the source. For avoiding the fast and random phase locking between the signal and local oscillator in experiment, we also analyze the security of four-state protocol using no-switching scheme.
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.
We investigate the security of reverse reconciliation two-way continuous-variable quantum key distribution with source noise at both legitimate sides. Because the source noise originates from imperfect devices, we ascribe it to the legitimate sides rather than the eavesdropper. The trusted model consists of a thermal noise injected into a beam splitter. The expressions of secret key rate are derived against collective entangling cloner attacks for homodyne and heterodyne detections. Simulation results show that by applying the trusted model, the security bound of the reverse reconciliation two-way protocols can be tightened, while the advantage over one-way protocols still maintains.
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.