  Quantum Key Distribution (QKD) provides an efficient means to exchange
information in an unconditionally secure way. Historically, QKD protocols have
been based on binary signal formats, such as two polarisation states, and the
transmitted information efficiency of the quantum key is intrinsically limited
to 1 bit/photon. Here we propose and experimentally demonstrate, for the first
time, a high-dimensional QKD protocol based on space division multiplexing in
multicore fiber using silicon photonic integrated lightwave circuits. We
successfully realized three mutually unbiased bases in a four-dimensional
Hilbert space, and achieved low and stable quantum bit error rate well below
both coherent attack and individual attack limits. Compared to previous
demonstrations, the use of a multicore fiber in our protocol provides a much
more efficient way to create high-dimensional quantum states, and enables
breaking the information efficiency limit of traditional QKD protocols. In
addition, the silicon photonic circuits used in our work integrate variable
optical attenuators, highly efficient multicore fiber couplers, and
Mach-Zehnder interferometers, enabling manipulating high-dimensional quantum
states in a compact and stable means. Our demonstration pave the way to utilize
state-of-the-art multicore fibers for long distance high-dimensional QKD, and
boost silicon photonics for high information efficiency quantum communications.
