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Frontiers in Optics

Virtual Photon Subtraction with Noisy Source in Continuous-Variable Quantum Key Distribution

Zhengyu Li, Xiang Peng, Hong Mei Guo

Published Jan 1, 2015• 0 citations
Publisher

Abstract

We propose a non-Gaussian postselection method to emulate the photon subtraction in continuous-variable quantum key distribution which extends the transmission distance. A method to further improve the performance for noisy source is also presented.
DOI
10.1364/fio.2015.jw2a.46

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Photon subtraction can enhance the performance of continuous-variable quantum key distribution (CV QKD). However, the enhancement effect will be reduced by the imperfections of practical devices, especially the limited efficiency of a single-photon detector. In this paper, we propose a non-Gaussian postselection method to emulate the photon substraction used in coherent-state CV QKD protocols. The virtual photon subtraction not only can avoid the complexity and imperfections of a practical photon-subtraction operation, which extends the secure transmission distance as the ideal case does, but also can be adjusted flexibly according to the channel parameters to optimize the performance. Furthermore, our preliminary tests on the information reconciliation suggest that in the low signal-to-noise ratio regime, the performance of reconciliating the postselected non-Gaussian data is better than that of the Gaussian data, which implies the feasibility of implementing this method practically.
The method of improving the performance of continuous-variable quantum key distribution protocols by postselection has been recently proposed and verified. In continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocols, the measurement results are obtained from untrusted third party Charlie. There is still not an effective method of improving CV-MDI QKD by the postselection with untrusted measurement. We propose a method to improve the performance of coherent-state CV-MDI QKD protocol by virtual photon subtraction via non-Gaussian postselection. The non-Gaussian postselection of transmitted data is equivalent to an ideal photon subtraction on the two-mode squeezed vacuum state, which is favorable to enhance the performance of CV-MDI QKD. In CV-MDI QKD protocol with non-Gaussian postselection, two users select their own data independently. We demonstrate that the optimal performance of the renovated CV-MDI QKD protocol is obtained with the transmitted data only selected by Alice. By setting appropriate parameters of the virtual photon subtraction, the secret key rate and tolerable excess noise are both improved at long transmission distance. The method provides an effective optimization scheme for the application of CV-MDI QKD protocols.
It is shown that the non-Gaussian operations can not only be used to prepare the nonclassical states, but also to improve the entanglement degree between Gaussian states. Thus these operations are naturally considered to enhance the performance of continuous variable quantum key distribution (CVQKD), in which the non-Gaussian operations are usually placed on the right-side of the entangled source. Here we propose another scheme for further improving the performance of CVQKD with the entangled-based scheme by operating photon-addition operation on the left-side of the entangled source. It is found that the photon-addition operation on the left-side presents both higher success probability and better secure key rate and transmission distance than the photon subtraction on the right-side, although they share the same maximal tolerable noise. In addition, compared to both photon subtraction and photon addition on the right-side, our scheme shows the best performance and the photon addition on the right-side is the worst.
A suitable photon-subtraction operation can be exploited to improve the maximal transmission of continuous-variable quantum key distribution (CVQKD) in point-to-point quantum communication. Unfortunately, the photon-subtraction operation faces solving the improvement transmission problem of practical quantum networks, where the entangled source is located in the third part, which may be controlled by a malicious eavesdropper, instead of in one of the trusted parts, controlled by Alice or Bob. In this paper, we show that a solution can come from using a non-Gaussian operation, in particular, the photon-subtraction operation, which provides a method to enhance the performance of entanglement-based (EB) CVQKD. Photon subtraction not only can lengthen the maximal transmission distance by increasing the signal-to-noise rate but also can be easily implemented with existing technologies. Security analysis shows that CVQKD with an entangled source in the middle (ESIM) from applying photon subtraction can well increase the secure transmission distance in both direct and reverse reconciliations of the EB-CVQKD scheme, even if the entangled source originates from an untrusted part. Moreover, it can defend against the inner-source attack, which is a specific attack by an untrusted entangled source in the framework of ESIM.
It has been found that non-Gaussian operations can be applied to increase and distill entanglement between Gaussian entangled states. We propose here a method to improve the performance of entanglement-based (EB) continuous-variable quantum-key-distribution protocol by using the non-Gaussian operation, in particular, the subtraction operation, which can be implemented under current technology easily. Security analysis shows that the subtraction operation can well increase the secure distance and tolerable excess noise of the EB scheme and also the corresponding prepare-and-measure scheme.
Quantum key distribution (QKD) with continuous variable (CV) is an effective method for achieving the high key rate, but is also limited to a short transmission distance. To overcome this limitation, some solutions have been proposed, including non-Gaussian operations, such as photon addition and photon subtraction using ideal photon source and number-resolving detection. Here we consider the effect of non-Gaussian operation for realistic photon source and ideal on-off photon detection. In the realistic case, it is shown that the performance of CVQKD can not be improved by both photon-subtraction/addition on the right side before the entangled source reaches the channel and photon-subtraction on the left side preceding the entangled source to the sender Alice before performing heterodyne detection, but be enhanced by the photon addition on the left side in a long distance case. These results may provide a useful reference for quantum information with continuous variable.