We propose and experimentally demonstrate a novel, to the best of our knowledge, correlated random bit generation (CRBG) scheme in virtue of the synchronization of two physical entropy sources that are composed of a continuous-wave laser, a phase modulator that is driven by the output of a local laser subject to constant-amplitude and random-phase (CARP) injection, as well as a dispersive component. It is experimentally indicated that wideband complex physical entropy sources with an effective bandwidth of 22 GHz can be achieved, and high-quality synchronization with a large cross-correlation coefficient (similar to 0.95) can be achieved by introducing symmetric CARP injections into the local lasers at Alice and Bob ends. Based on this, two distributed CRBSs with a bit rate over 3 Gb/s and satisfactory consistency are independently generated at Mice and Bob ends; the excellent randomness of CRBSs is verified using a test suite of the National Institute of Standards and Technology. (C) 2019 Optical Society of America