# Noiseless Attenuation for Continuous-Variable Quantum Key Distribution over Ground-Satellite Uplink
## 1 Introduction  
In recent decades, a number of quantum cryptography protocols have been successfully realized, including quantum teleportation (QT) [1, 2], quantum key distribution (QKD) [3], quantum secret sharing [4, 5, 6], and quantum coding [7, 8]. QKD, which mainly relies on [PERSON]'s uncertainty principle, which provide us with an unconditional secure method for private information transmission over an insecure channel. Generally, it can be divided into two categories, referred to as discrete-variable (DV) QKD [9] and continuous-variable (CV) QKD [10]. In DV-QKD, the information is usually encoded in the polarization or time bin of single photons, using expensive and extreme cryo-cooling single-photon detectors [11]. Compared with DV-QKD, CV-QKD, which involves the coherent state, can achieve higher channel capacity by using homodyne or heterodyne detection, and has good compatibility with standard optical communications [12]. To date, CV-QKD has been successfully analyzed in fiber links both theoretical and experimental [13, 14]. However, due to heavy losses in the practical fiber, the distance over which the coherent state of light can be transmitted is restricted within hundreds of kilometers. So far, the longest transmission distance of CV-QKD is only 202.81 km [3]. Since it is difficult to noiselessly amplify the quantum state at the receiver [15], exhibiting a global-scale network through a fiber link becomes a challenge. In the last few years, the research towards global-scale network has increased for a satellite-mediated scenario [16], where the channel losses are limited since the effective thickness of the atmosphere is only about 20 km [17]. The major works are being performed in downlink configuration, however, an uplink from ground to a quantum satellite is less explored because the atmosphericturbulence acts on early stages of optical signal transmission, leading to a larger diffraction-induced broadening and more serious beam wandering [18]. As has been pointed out, the secret key rate in uplink is less than one order of magnitude compared with the downlink scenario [19]. Despite the inferior performance compared with that of the downlink, the uplink CV-QKD is also of great value owing to the simple satellite structure, the variability of quantum sources, and the accessibility for maintenance repair [20; 21]. To improve the performance of the uplink CV-QKD, we consider an enhanced source preparation scheme involving the noiseless attenuation (NA) operation [22]. The NA operation has been used for quantum key distribution, quantum teleportation, and other applications to reduce the detrimental effects of channel losses [23; 24; 25]. On the premise of the previous achievements, in this paper, we suggest an NA-based enhancement scheme for the Gaussian-modulated coherent-state protocol of uplink. Due to the limited space on the quantum satellite, the NA operation is applied to the ground station (the sender). We perform a suitable NA process by using a zero-photon catalysis (ZPC) operation, which happens to be a zero-energy-input operation that does not introduce the consumption of external energy [26]. We prove the security of the NA-based CV-QKD protocol against the Gaussian collective attack under both the asymptotic case and finite-size regime. Our results show that both the allowable zenith angle and effective communication time are improved compared with the traditional CV-QKD protocol. The research confirms the role of the NA operation on the uplink CV-QKD protocol and is conducive to making the CV-QKD protocol more practical. The paper is organized as follows. In Section 2, we illustrate characteristics of the uplink CV-QKD system. In Section 3, we suggest the NA-based source preparation scheme, based on zero-photon catalysis, for improving the performance of the CV-QKD system. Section 4 shows the security of the NA-based protocol under both the asymptotic case and the finite-size regime. Finally, conclusions are drawn in Section 5.