# Free-Space QKD with Modulating Retroreflectors Based on the B92 Protocol
## 1 Introduction  
Quantum key distribution (QKD) can help two distant parties to realize theoretical unconditional security communication [1]. QKD can be categorized into fiber-based QKD and free-space QKD according to different communication channels. The longest transmission distance that fiber-based QKD can achieve is only hundreds of kilometers because of the intrinsic loss of the fiber (approximately 0.2 dB/km@1550 nm) [2; 3; 4]. Conversely, free-space QKD can achieve a transmission distance of thousands of kilometers owing to its lower channel loss, and it is also suitable for mobile communication owing to its flexible link [5; 6; 7]. A worldwide quantum-secured communication network is foreseeable by integrating free-space and fiber-based QKD [8].  
Despite encouraging advances in free-space QKD [9; 10], many challenges remain, for example, the contradiction between the limited payload of satellites and the complex structure of free-space QKD system [6]. The miniaturization and light weight of QKD systems has become an important topic [11; 12]. Cheaper microsatellites, such as standardized CubeSats, will play a greater role in future quantum networks [13; 14; 15]. Free-space QKD using modulating retro-reflectors (MRR-QKD) significantly reduces the pointing requirement and simplifies the structure of the mobile terminal, therefore decreasing the payload greatly, which may be a prospective scheme.  
In the MRR-QKD system, two communication parties are defined as the interrogator and MRR terminal. Compared with the traditional QKD system, the structure of the MRR terminal in the MRR-QKD system is simpler, and the pointing requirement is reduced significantly(more than three orders of magnitude) [16]. The concept of MRR-QKD was firstproposed by [PERSON] in 2002 [17]. [PERSON] demonstrated an imperfect experiment for satellite-to-ground MRR-QKD between low earth orbit (LEO) satellites and the Matera Laser Ranging Observatory (MLRO) [18]. Many studies have been conducted recently [16; 19; 20]. In 2017, [PERSON] designed a practical MRR-QKD system and achieved a quantum bit error rate (QBER) of approximately 5% with a modulation rate of 1 MHz in the laboratory [16].  
The MRR-QKD system of [PERSON] [16], which we will call RM2018 in this paper, uses up to eight multiple quantum wells (MQW) [21; 22] intensity modulators to realize polarization modulation. Owing to the finite extinction ratio [23] of MQW modulators, there is leakage noise in this system, which causes higher QBER. Based on the superposition of two mutually perpendicular waves [24], we proposed a MRR-QKD system based on the B92 protocol [25]. Our scheme reduced the complexity of the system structure and eliminated leakage noise. The remainder of this paper is organized as follows. In Section 2, we introduce the configuration of our MRR-QKD system and its mathematical model. In Section 3, the performance of the system under different extinction ratios and optical misalignment errors is studied and compared with previous works. In Section 4, we discuss our results. In Section 5, we present our conclusions.