The homodyne-detected transient four-wave-mixing response of InAs/GaAs self-assembled quantum dots shows temporal oscillations of the optically induced Raman coherence arising from two entangled polarization eigenstates of the exciton. The phase sensitive nature of the homodyne detection enables us to follow the time evolution of the nonradiative quantum coherence between the polarization states, providing a measurement of the fine-structure splitting in the dots, which is much less than the inhomogeneous broadening, and the corresponding decoherence rate of the entangled state.