  We present a comprehensive framework for quantum state tomography (QST) of
time-bin qudits sent through a fiber. Starting from basic assumptions, we
define a positive-operator valued measure (POVM) which is then applied to the
quantum state reconstruction problem. A realistic scenario is considered where
the time uncertainty of the detector is treated as a source of experimental
noise. The performance of the quantum tomography framework is examined through
a series of numerical simulations conducted for different parameters describing
the apparatus. The quality of state recovery, quantified by the notion of
minimum fidelity, is depicted on graphs for a range of fiber lengths. Special
attention is paid to relative phase reconstruction for qubits and qutrits. The
results present relevant interdependence between the fiber length and the
detector jitter.
