Quantum key distribution (QKD) is regarded as an alternative to traditional cryptography methods for securing data communication by quantum mechanics rather than computational complexity. Towards the massive deployment of QKD, embedding it with the telecommunication system is crucially important. Homogenous optical multi-core fibers (MCFs) compatible with spatial division multiplexing (SDM) are essential components for the next-generation optical communication infrastructure, which provides a big potential for co-existence of optical telecommunication systems and QKD. However, the QKD channel is extremely vulnerable due to the fact that the quantum states can be annihilated by noise during signal propagation. Thus, investigation of telecom compatibility for QKD co-existing with high-speed classical communication in SDM transmission media is needed. In this paper, we present analytical models of the noise sources in QKD links over heterogeneous MCFs. Spontaneous Raman scattering and inter-core crosstalk are experimentally characterized over spans of MCFs with different refractive index profiles, emulating shared telecom traffic conditions. Lower bounds for the secret key rates and quantum bit error rate (QBER) due to different core/wavelength allocation are obtained to validate intra- and inter-core co-existence of QKD and classical telecommunication.