  In this paper, we investigate the effects of chromatic dispersion on the
temporal wave functions (TWFs) of single photons in the context of quantum
communications. We start by considering TWFs defined by generalized Gaussian
modes. From this framework, we derive two specific models: chirped and
unchirped Gaussian TWFs. In the first case, we explore the impact of the chirp
parameter on the properties of single-photon TWFs. We show that by properly
adjusting the chirp parameter, it is possible to compensate for the detrimental
effects of chromatic dispersion, allowing for the maintenance of high-fidelity
transmission of quantum information over long distances. Furthermore, we
examine the effects of chromatic dispersion on a qubit defined in the time
domain, illustrating how this phenomenon can influence the transmission of
information encoded in time-bins. Finally, we consider non-Gaussian TWFs that
are represented by hyperbolic-secant modes. Our results provide important
insights into the design and implementation of high-speed and long-distance
quantum communication systems. The findings underscore the potential for using
chirp management techniques to mitigate the effects of chromatic dispersion.
