  The first measurement of event-by-event antideuteron number fluctuations in
high energy heavy-ion collisions is presented. The measurements are carried out
at midrapidity ($|\eta| < 0.8$) as a function of collision centrality in
Pb$-$Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV using the ALICE detector.
A significant negative correlation between the produced antiprotons and
antideuterons is observed in all collision centralities. The results are
compared with a state-of-the-art coalescence calculation. While it describes
the ratio of higher order cumulants of the antideuteron multiplicity
distribution, it fails to describe quantitatively the magnitude of the
correlation between antiproton and antideuteron production. On the other hand,
thermal-statistical model calculations describe all the measured observables
within uncertainties only for correlation volumes that are different with
respect to those describing proton yields and a similar measurement of
net-proton number fluctuations.
