  Using the nucleon coalescence model based on kinetic freeze-out nucleons from
the hybrid model of MUSIC hydrodynamics and UrQMD hadronic transport, we study
the production of anti-deuteron and its event-by-event fluctuation in Pb+Pb
collisions at $\sqrt{s_{NN}}=5.02$ TeV. We find a clear suppression of the
anti-deuteron to antiproton yield ratio in peripheral collisions, which is in
accordance with the measurements from the ALICE Collaboration. Also found is a
Poissonian event-by-event fluctuation of the anti-deuteron multiplicity
distribution in all collision centralities, which is different from the
prediction of a simple coalescence model calculation that assumes all
antiproton and antineutron pairs to have the same probability to form
anti-deuterons. We further find a small negative correlation between the
anti-deuteron and antiproton multiplicity distributions as a result of the
baryon conservation.
