In this paper, we propose several entanglement assisted QKD protocols based on time-energy encoding with the number of mutually unbiased bases (MUBs) larger than two. We describe how to implement these protocols based on: (i) optical FFT device implemented in integrated optics with the help of Franson interferometers and (ii) Weyl gate. We also describe the corresponding weak-coherent state-based protocol. By employing the N-dimensional pulse position modulation (ND-PPM) approach, the secret key rate of single photon pulse per signaling interval protocols can be improved by N/log2N times. However, the corresponding entanglement assisted protocols require the use of cavity quantum electrodynamics (CQED) principles to further entangle single photon pulse per frame state. We then analyze the security of the proposed protocols and provide the finite secret key rates in the presence of various imperfections including background errors and timing jitter, for which we propose the K-neighbor model. Finally, we provide the improvements in secret key rates of proposed protocol over conventional two-base time-energy QKD protocol.