While quantum key distribution (QKD) based on two-dimensional (qubit) encoding is a mature, field-tested technology, its performance is lacking for many cryptographic applications. High-dimensional encoding for QKD enables increased achievable key rates and robustness as compared to the standard qubit-based systems. However, experimental implementations of such systems are more complicated, expensive, and require careful security analysis as they are less common. In this work, we present a proof-of-principle high-dimensional time-phase BB84 QKD experiment using only one single-photon detector per measurement basis. We employ the temporal Talbot effect to detect QKD symbols in the control basis and show experimentally obtained simplistic key rates for the two-dimensional and four-dimensional cases, including in an urban fiber network. We present a comparison of a simplistic secret key rate obtained from a standard security proof with the one derived from a recently devised proof using a tunable beam splitter to display security issues stemming from asymmetric detection efficiencies in the two bases. Our results contribute to the discussion of the benefits of high-dimensional encoding and highlight the impact of security analysis on the achievable QKD performance.
