# Performance Analysis of Continuous-Variable Quantum Key Distribution with Multi-Core Fiber
## 1 Introduction  
Since [PERSON] and [PERSON] presented the first quantum key distribution (QKD) protocol, i.e., BB84 protocol [1], lots of groundbreaking researches of QKD have emerged. The previous QKD was based on discrete variable (DV) that encodes information into a single photon state. However, the generation and detection of single photons still remain a significant technology challenge in DVQKD. Fortunately, an alternative approach, continuous-variable (CV) QKD [2], was proposed as it can be compatible with mature components and technologies of classical communication, resulting in high detection efficiency. CVQKD has been proved to be secure against general collective attacks, which are optimal in both the asymptotic case [3, 4] and the finite-size regime [5, 6, 7]. To lift the security loopholes of the local oscillator (LO) and the detector, the locally generated LO schemes [8, 9, 10] and the measurement-device-independent (MDI) schemes [11, 12, 13] have been proposed recently. In experiments, long distance of up to 150 km [14], high speed of up to 12 Mbit/s [15] and high security MDI quantum cryptography [16] in CVQKD have also been achieved.  
In the last decade, theoretical performance analysis of CVQKD has been suggested [17, 18, 19, 20, 21, 22, 23, 24]. Moreover, multiplexing technologies, which are based on wavelength, polarization, phase and orbital angular momentum, have been demonstrated for the CVQKD system to improve its performance [15, 25, 26, 27]. However, the rate at present is far from meeting the needs of the practical implementation. How to increase the secret key rate is still worthy of further investigation. In the lastfew years, to avoid a capacity crunch in the single-mode fiber (SMF), space-division multiplexing (SDM) technique has been proposed to further increase the data bandwidth in classical communications. One realizing approach of SDM is to use multi-core fiber (MCF). Through using it, another multiplexing dimensionality--spatial dimension--is able to be fully utilized to increase the secret key rate. The contained cores of the MCF can be exploited as parallel channels for independent signals and hence the data bandwidth can be multiplied. Recently, experimental demonstration has been made for DVQKD based on the SDM technique over a MCF [28; 29; 30], which opens a way for CVQKD to break through the bottleneck of the secret key rate in the traditional SMF-based system.  
In this paper, we propose the MCF-based CVQKD scheme, which can increase the secret key rate via transmitting multiple spatial modes simultaneously. The excess noise contributed by the inter-core crosstalk between cores can be effectively suppressed by using quantum channel wavelength management between cores. As extra optical devices of the fan-in/fan-out (FIFO) should be used at the input and output of the fiber, the insert loss of these devices should also be considered. We perform simulations based on the Gaussian-modulated coherent state CVQKD protocol and numeric results show that the performance of the one-way and two-way protocols for each core may be slightly degraded because of the insert loss of the FIFO, but the total secret key rate can be significantly improved. However, the performance of the MDI CVQKD protocol will be degraded due to the effect of the insert loss of the FIFO.  
This paper is arranged as follows. In Section 2, we show the channel characteristic of the MCF-based CVQKD. In Section 3, we present the performance analysis of the MCF-based CVQKD protocols in terms of the secure key rate. Finally, we draw conclusion in Section 4.