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Synchronization phenomena of two chaotically emitting semiconductor lasers subject to delayed optical feedback are investigated. The lasers are unidirectionally coupled via their optical fields. Our experimental and numerical studies demonstrate that the relative optical feedback phase is of decisive importance: a characteristic synchronization scenario evolves under variation of the relative optical-feedback phase mediating cyclically between chaos synchronization in conjunction with coherent fields, and uncorrelated states in conjunction with incoherent fields. As a key result, we propose, and numerically demonstrate, a novel ON/OFF phase shift keying method opening up new perspectives for applications in communication systems using chaotic carriers.