Chaos data analysis has been performed on the chaotic output power time series data from a synchronized transmitter-receiver pair of semiconductor lasers. The system uses an asymmetric, bidirectional coupling configuration between the master (transmitter), which is a laser diode with optical feedback, and a stand-alone slave semiconductor laser. The correlation dimension of the chaotic time series has a minimum value of 4, which was obtained from high-bandwidth measurements. The correlation dimensions for both the master and the synchronized slave are identical when the cross-correlation coefficient of the synchronized chaos is above 0.9. These results establish correlation dimension analysis as an effective tool for the determination of the quality of wideband chaos synchronization.