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Chaotic spatiotemporal dynamics generated by a nonlinear set of coupled partial differential equations are synchronized via a scalar complex variable. Our results show that synchronization is robust to noise, and we demonstrate chaotic communication in a high-dimensional system. We have also discovered that the added dimensionality creates a new quasisynchronous state, enabling the transmission of multiple messages through a single scalar complex channel. The feasibility of these novel ideas is demonstrated on a realistic numerical model of chaotic semiconductor lasers.