  The coexistence of quantum and classical light in the same fiber link is
extremely desired in developing quantum communication. It has been implemented
for different quantum information tasks, such as classical light coexisting
with polarization-entangled photons at telecom O-band, and with quantum signal
based quantum key distribution (QKD). In this work, we demonstrate the
coexistence of energy-time entanglement based QKD and fiber optical
communication at the telecom C-band. The property of noise from the classical
channel is characterized with classical light at different wavelengths. With
the largest noise, i.e., the worst case, the properties of energy-time
entanglement are measured at different fiber optical communication rates. By
measuring the two-photon interference of energy-time entanglement, our results
show that a visibility of 82.01$\pm$1.10\% is achieved with a bidirectional 20
Gbps fiber optical communication over 40 km. Furthermore, by performing the
BBM92 protocol for QKD, a secret key rate of 245 bits per second could be
generated with a quantum bit error rate of 8.88\% with the coexisted
energy-time entanglement.~Our demonstration paves the way for developing the
infrastructure for quantum networks compatible with fiber optical
communication.
