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For secure practical systems, quantum key distribution (QKD) must provide high key rates over long distances. Time-entanglement-based QKD promises to increase the secret key rate and distribution distances compared to other QKD implementations. This article describes the major steps in QKD protocols, focusing on the nascent QKD technology based on high-dimensional time-bin entangled photons. We overview the state-of-the-art from the information and coding theory perspective. In particular, we discuss the key rate loss due to single-photon detector imperfections. We hope the open questions posed and discussed in this article will inspire information and coding theorists to contribute to and impact fledgling quantum applications and influence future quantum communication systems.