  An important tool in studying the sub-femtoscale spacetime structure of
matter in ultrarelativistic heavy-ion collisions is Hanbury-Brown-Twiss (HBT)
intensity interferometry of identical particles in the final state of such
collisions. We show here that a variant of an entanglement enabled intensity
interferometry ($E^2 I^2$) proposed by Cotler and Wilczek provides a powerful
alternative to HBT interferometry in extracting fundamental nonperturbative
features of QCD at high energies. In particular, we show that the spatial
distributions of color singlet (pomeron) configurations in nuclei can be
obtained from exclusive resonant decays of $\rho$-mesons into $\pi^\pm$-pairs
in ultrarelativistic ultraperipheral nuclear collisions (UPCs) at RHIC and the
LHC. The $E^2 I^2$ framework developed here is quite general. It can be
employed to extract information on the spin structure of pomeron couplings as
well as enhance the discovery potential for rare odderon configurations from
exclusive vector meson decays into few-particle final states both in UPCs and
at the Electron-Ion Collider.
