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arXiv:1810.11457 · Physical Review A

Secret key rate of a continuous-variable quantum-key-distribution scheme when the detection process is inaccessible to eavesdroppers

Ryo Namiki, Akira Kitagawa, Takuya Hirano

Published Oct 15, 2018• 7 citations
arXivHTMLPDF

Abstract

We have developed a method to calculate a secret key rate of a continuous-variable quantum-key-distribution scheme using four coherent states and postselection for a general model of Gaussian attacks. We assume that the transmission line and detection process are described by a pair of Gaussian channels. In our analysis, while the loss and noise on the transmission line are induced by an eavesdropper, Eve, who can replace the transmission line with a lossless and noiseless optical fiber, she is assumed inaccessible to the detection process. By separating the transmission noise and detection noise, we can always extract a larger key compared with the case that all loss and noises are induced by an eavesdropper's interference. An asymptotic key rate against collective Gaussian attacks can be determined numerically for the given channels' parameters. The improvement of the key rates turns out to be more significant for the reverse-reconciliation scheme.

DOI
10.1103/physreva.98.042319

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We have developed a method to calculate a secret key rate of a continuous-variable quantum-key-distribution scheme using four coherent states and postselection for a general model of Gaussian attacks. We assume that the transmission line and detection process are described by a pair of Gaussian channels. In our analysis, while the loss and noise on the transmission line are induced by an eavesdropper, Eve, who can replace the transmission line with a lossless and noiseless optical fiber, she is assumed inaccessible to the detection process. By separating the transmission noise and detection noise, we can always extract a larger key compared with the case that all loss and noises are induced by an eavesdropper's interference. An asymptotic key rate against collective Gaussian attacks can be determined numerically for the given channels' parameters. The improvement of the key rates turns out to be more significant for the reverse-reconciliation scheme.
We develop a physical model to describe the signal transmission for a continuous-variable quantum key distribution scheme and investigate its security against a couple of eavesdropping attacks assuming that the eavesdropper’s power is partly restricted owing to today’s technological limitations. We consider an eavesdropper performing quantum optical homodyne measurement on the signal obtained by a type of beamsplitting attack. We also consider the case in which the eavesdropper Eve is unable to access a quantum memory and she performs heterodyne measurement on her signal without performing a delayed measurement. Our formulation includes a model in which the receiver’s loss and noise are unaccessible by the eavesdropper. This setup enables us to investigate the condition that Eve uses a practical fiber differently from the usual beamsplitting attack where she can deploy a lossless transmission channel. The secret key rates are calculated in both the direct and reverse reconciliation scenarios.
We investigate the security against collective attacks of a continuous variable quantum key distribution scheme in the asymptotic key limit for a realistic setting. The quantum channel connecting the two honest parties is assumed to be lossy and imposes Gaussian noise on the observed quadrature distributions. Secret key rates are given for direct and reverse reconciliation schemes including post-selection in the collective attack scenario. The effect of a nonideal error correction and two-way communication in the classical post-processing step is also taken into account.
Abstract Gaussian-modulated coherent-state (GMCS) continuous-variable quantum key distribution (CV-QKD) offers a practical path to quantum-secured communication owing to its compatibility with existing optical fibre networks and use of mature security proofs. Achieving high secret key rates in real-time systems, however, requires post-processing schemes that are both information-theoretically efficient and computationally scalable. In previous experimental work 1 , we have demonstrated record real-time key rates using a one-round sliced reconciliation scheme with guard-band post-selection. Here, we present the corresponding theoretical framework and provide an asymptotic security analysis that considers arbitrary collective attacks, a much broader class of attacks than the usually assumed Gaussian collective attacks. The security analysis applies the entropic continuity of quantum channels justified by a quantum channel estimation procedure. In conditions of high noise, our scheme uses 500 times less classical communication than multidimensional reconciliation.
A novel quantum key distribution (QKD) protocol is proposed and demonstrated. It is based on the transmission of Gaussian-modulated coherent states that are laser pulses containing a few hundred photons .Shot-noise limited coherent (homodyne) detection is used, which makes it possible to achieve high secret-key rates. It remains, in principle, efficient for any value of the line transmission by use of a "reverse reconciliation" technique, which is shown to be secure against individual attacks based on entanglement and quantum memories. The basic idea is to use a reverse reconciliation protocol, that is, Alice attempts to guess what was received by Bob rather than Bob guessing what was sent by Alice. A reverse protocol always gives Alice an advantage over a potential eavesdropper Eve, regardless the line loss. In addition, a specific advantage of using quantum continuous variables is that the high dimensionality of the phase space may be exploited by modulating the field quadratures with a large dynamics, allowing the encoding of several key bits per pulse. This, together with the fact that fast modulation and detection can be achieved, results in a high-rate secret key distribution.
We designed high-efficiency error correcting codes allowing us to extract an errorless secret key in a continuous-variable quantum key distribution (CVQKD) protocol using a Gaussian modulation of coherent states and a homodyne detection. These codes are available for a wide range of signal-to-noise ratios on an additive white Gaussian noise channel with a binary modulation and can be combined with a multidimensional reconciliation method proven secure against arbitrary collective attacks. This improved reconciliation procedure considerably extends the secure range of a CVQKD with a Gaussian modulation, giving a secret key rate of about ${10}^{\ensuremath{-}3}$ bit per pulse at a distance of 120 km for reasonable physical parameters.