  We present a method for measuring quantum states encoded in the temporal
modes of photons. The basis for the multilevel quantum states is defined by the
use of modes propagating in a dispersive medium, which is a fiber in this case.
The propagation and time-resolved single photon detection allow us to define a
positive-operator valued measure (POVM). The POVM depends on the amount of
dispersion and the characteristics of a detector. This framework is numerically
tested by performing quantum state tomography on a large number of states for a
set of realistic experimental settings. Finally, the average fidelity between
the expected and reconstructed states is computed for qubits, qutrits and
entangled qubits.

Quantum Physics