  We present results of correlated pseudopotential calculations of an exciton
in a pair of vertically stacked InGaAs/GaAs dots. Competing effects of strain,
geometry, and band mixing lead to many unexpected features missing in
contemporary models. The first four excitonic states are all optically active
at small interdot separation, due to the broken symmetry of the single-particle
states. We quantify the degree of entanglement of the exciton wavefunctions and
show its sensitivity to interdot separation. We suggest ways to
spectroscopically identify and maximize the entanglement of exciton states.
