Photon-Efficient Energy-Time Entanglement QKD Using Spatially-Coupled Irregular-Repeat-Accumulate Error Correction Codes*

High-dimensional quantum key distribution (QKD) protocols based on energy-time entangled photons are unique thanks to their high bits per photon efficiency, due to infinite Hilbert space. However, for demanding QKD channels, pumping the entanglement source higher to increase raw key rate inevitably leads to a larger fraction of uniformly distributed errors, originating from an increased background and multi-photon emissions, which necessitates robust ECC schemes. Previous QKD error correction studies utilize widespread multi-level-coding (MLC) low-density parity-check coding, which is binary by design and independently corrects each bit layer. In this work, we developed non-binary spatially-coupled (SC) irregular repeat accumulate (IRA) codes that we strategically combine two advanced low-density-parity-check (LDPC) codes, the SC codes and the IRA codes. These SC-IRA codes are tailored for the energy-time entangled QKD channels through the proposed optimization framework. Our simulation results show that SC-IRA codes can reach up to 20.62% higher photon efficiency than the MLC scheme. We will utilize our Mbit/s level high-alphabet time-bin encoding testbed to demonstrate SC-IRA advantage up to 10-bits encoding.