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We demonstrate coupling and entangling of quantum states in a pair of vertically aligned, self-assembled quantum dots by studying the emission of an interacting electron-hole pair (exciton) in a single dot molecule as a function of the separation between the dots. An interaction-induced energy splitting of the exciton is observed that exceeds 30 millielectron volts for a dot layer separation of 4 nanometers. The results are interpreted by mapping the tunneling of a particle in a double dot to the problem of a single spin. The electron-hole complex is shown to be equivalent to entangled states of two interacting spins.