# Improving Eight-State Continuous Variable Quantum Key Distribution by Applying Photon Subtraction
## 1 Introduction  
Two independent long-distance legitimate communicators, say, [PERSON]'s station and [PERSON]'s station, can generate an unordered security key sequence through the untrusted quantum and traditional electronic channels by using quantum key distribution (QKD) [1; 2]. The fundamental laws of quantum mechanics ensure their absolute security [3; 4]. The traditional QKD protocol is usually divided into the following three categories: The discrete variable (DV) QKD protocol, which encodes information based on the polarization states of a single photon. The second is the continuous variable (CV) QKD protocol [5; 6; 7; 8], which encodes key bits in the quadrature of the optical field. The third is the distributed phase reference (DPR) QKD protocol; its main implementation is to use weak coherent pulses to pass information. Unlike DVQKD, in CVQKD there is no necessity to use a single photon detector. Additionally, the security of CVQKD against collective attacks [9; 10] and coherent attacks has been proved. Therefore, it can provide a more cost-effective solution, in practice, than its DVQKD counterpart [11]. While the DPRQKD protocol has been used in real settings for many years, it has never been completely secure [12].  
Generally speaking, CVQKD can be mainly divided into two categories: Discrete modulation CVQKD [13] and Gaussian modulation CVQKD [14]. However, in the context of long-distance communication, in Gaussian modulation CVQKD it is difficult to harmonize the Gaussian variable required for modulation in the presence of a low SNR. Fortunately, there is no such limitation for discretely-modulated CVQKD protocols. It is worth noting that the current four-state CVQKD has been proven secure during an anti-collective attack, which has been experimentally demonstrated [15; 16; 17]. Recently, another discretely-modulated scheme, called the eight-state CVQKD, has been proposed, which shows better performance compared with the four-state CVQKD [18; 19].  
Non-Gaussian operations (including photon addition and photon subtraction) have been diffusely studied in both theory and experiments. By taking advantage of these operations, the entanglement of an Gaussian entangled state is improved and distilled, and thus the maximum secure distance iswell-enhanced [20; 21; 22]. The implementation of a photon subtraction operation is simple, as it can be smoothly performed with optical beam splitters and photon detectors. In this paper, we deployed a photon subtraction operation on [PERSON]'s side, in order to effectively improve the performance of the eight-state protocol. A security analysis shows that the performance of the eight-state protocol can be improved with proper photon subtraction.  
The structure of this paper is as follows. In Section 2, we introduce the original eight-state CVQKD protocol, and then introduce the modified protocol (applying a photon-subtraction operation). In Section 3, we perform a security analysis of the modified protocol. Simulation results are illustrated in Section 4. Finally, the conclusion is drawn in Section 5.