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arXiv:0812.4314 · Journal of Physics B Atomic Molecular and Optical Physics

Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers

Simon Fossier, Eleni Diamanti, Thierry Debuisschert, Rosa Tualle-Brouri, Philippe Grangier

Published May 15, 2009• 256 citations
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Abstract

Continuous-variable quantum key distribution protocols have been implemented recently, based on Gaussian modulation of the quadratures of coherent states. A present limitation of such systems is the finite efficiency of the detectors, that can in principle be compensated for by the use of classical optical preamplifiers. Here we study this possibility in detail, by deriving the modified secret key generation rates when an optical parametric amplifier is placed at the output of the quantum channel. After presenting a general set of security proofs, we show that the use of preamplifiers does compensate all the imperfections of the detectors when the amplifier is optimal in terms of gain and noise. Imperfect amplifiers can also enhance the system performance, under conditions which are generally satisfied in practice.

DOI
10.1088/0953-4075/42/11/114014

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Continuous-variable quantum key distribution protocols have been implemented recently, based on Gaussian modulation of the quadratures of coherent states. A present limitation of such systems is the finite efficiency of the detectors, that can in principle be compensated for by the use of classical optical preamplifiers. Here we study this possibility in detail, by deriving the modified secret key generation rates when an optical parametric amplifier is placed at the output of the quantum channel. After presenting a general set of security proofs, we show that the use of preamplifiers does compensate all the imperfections of the detectors when the amplifier is optimal in terms of gain and noise. Imperfect amplifiers can also enhance the system performance, under conditions which are generally satisfied in practice.
Continuous-variable quantum key distribution protocols, based on Gaussian modulation of the quadratures of coherent states, have been implemented in recent experiments. A present limitation of such systems is the finite efficiency of the detectors, which can in principle be compensated for by the use of classical optical preamplifiers. Here we study this possibility in detail, by deriving the modified secret key generation rates when an optical parametric amplifier is placed at the output of the quantum channel. After presenting a general set of security proofs, we show that the use of preamplifiers does compensate for all the imperfections of the detectors when the amplifier is optimal in terms of gain and noise. Imperfect amplifiers can also enhance the system performance, under conditions which are generally satisfied in practice.
We propose a method to improve the secret key rates of four-state continuous-variable quantum key distribution by using an optical preamplifier. The modified protocol allows the distribution of higher secret key rates over long distances. Included in this paper is a detailed investigation of the effects of inserting an optical parametric amplifier into the output of the quantum channel in the four-state protocol, which will be instructive and meaningful about the usage of amplifiers in order to achieve the optimal performance of the protocol in a specific scenario.
Abstract Inherent defects of the detectors in a practical system cause deterioration of the performance of the unidimensional coherent-state continuous-variable quantum key distribution protocol. Aiming to achieve optimal performance, we propose a method of using a phase-sensitive amplifier to overcome the limitation that the detectors introduce. The modified protocol, corresponding to a higher key rate, provides the practical system with more robustness. To conduct a thorough investigation into the effects that the phase-sensitive amplifier creates, the expressions of the secret key rates are derived, under the conditions of coherent states, homodyne detection against collective attacks, and a phase-sensitive optical amplifier added at the output of the channel. Then, we carry out simulations to observe the performance in the cases of different gains. The simulation results demonstrate that the method we propose can improve the performance of the unidimensional protocol using coherent states and make up for the imperfections of the detector in a practical system.
The measurement-device-independent quantum key distribution (MDI-QKD) protocol is immune to imperfect measurement devices. However, its practicality and performance when implemented in continuous-variable (CV) mode are still not satisfactory. We propose a CV-MDI-QKD protocol based on modulated squeezed states, and analyze its security against two-mode Gaussian attack. The results show that the protocol can achieve a higher secret key rate and transmission distance than previous coherent-state and squeezed-state protocols. A method to compensate the imperfection of a practical homodyne detector using phase-sensitive optical amplifiers is also presented. By setting an appropriate optical amplification gain, realistic detectors with ordinary quantum efficiency can be employed. In addition, we discuss the impact of finite-size effects on the secret key rate of the protocol. The methods presented may aid in the practical application of the CV-MDI-QKD protocol.
That the simultaneous quantum key distribution and classical communication (SQCC) scheme are combined with the continuous variable quantum key distribution (CVQKD) and the classical communication together, will provide an effective method to implement the simultaneous CVQKD and the classical communication in the existing optical networks in the future. However, superimposing a classical signal on the quantum signal will introduce excess noise into the CVQKD system, thus greatly reducing the performance of the system. In this paper, a novel scheme of SQCC based on optical preamplifier (OPA) is proposed, that is, the OPA is inserted into the receiver to improve the performance of the system. On the one hand, under the condition of the same bit error rate, the amplification of the signal by the OPA can reduce the requirement for the modulation amplitude of the classical signal at the sending end, thereby reducing the noise effect of the classical signal on the quantum signal. On the other hand, the OPA can compensate for the imperfection of the receiver detector. Moreover, in the case of locally generated local oscillator, the amplifier can also amplify the weak phase reference pulse, and thus reducing the phase excess noise caused by the shot noise of the weak phase reference pulse. Numerical simulation results show that the proposed scheme has better performance than the original scheme in the sense of security key rate and transmission distance. These results show that this scheme provides an effective and practical method for the further development and practical application of the SQCC scheme.
In a practical quantum communication system, the security of signal source of continuous-variable quantum key distribution may be jeopardized due to device flaws and hidden attacks. In this paper, an improved scheme for Gaussian-modulated continuous-variable quantum key distribution based on an untrusted entangled source is proposed. In particular, the entanglement source is placed in an untrusted quantum channel to simulate that it is controlled by an eavesdropper, thereby verifying the security of Gaussian-modulated continuous-variable quantum key distribution in a complex environment. This work in detail analyzes the influence of untrusted entanglement source on practical Gaussian-modulated continuous-variable quantum key distribution system, and the numerical simulation shows that the performance of Gaussian-modulated continuous-variable quantum key distribution will dramatically decrease once the entanglement source has moved out of the sender, and it will slightly rise as the untrusted entanglement source slowly moves away from the sender. This paper further introduces two kinds of optical amplifiers, which are phase-sensitive amplifier and phase-insensitive amplifier, to compensate for the imperfection of the coherent detector. These amplifiers are beneficial to enhancing the quantum efficiency of the receiver’s detector. Specifically, the security key rate of Gaussian-modulated continuous-variable quantum key distribution with homodyne detection can be well improved by phase-sensitive amplifier, and the security key rate of Gaussian-modulated continuous-variable quantum key distribution with heterodyne detection can be well improved by phase-insensitive amplifier. To summary, this paper proposes a scheme for Gaussian-modulated continuous-variable quantum key distribution with untrusted entanglement source, experimental results show that the proposed scheme can generate secure quantum keys even if the Gaussian entanglement source is untrusted, and the two optical amplifiers can effectively improve the quantum efficiency of the detector at the receiver. This work aims to promote the practical process of the Gaussian-modulated continuous-variable quantum key distribution system and provide theoretical guidance for the practical implementation and application of the Gaussian-modulated continuous-variable quantum key distribution system.