Recent advances in non-Hermitian physical systems have led to numerous novel optical phenomena and applications. However, most realizations are limited to classical systems and quantum fluctuations of light is unexplored. For the first time, we report the observation of quantum correlations between light channels in an anti-symmetric optical system made of flying atoms. Two distant optical channels coupled dissipatively, display gain, phase sensitivity and quantum correlations with each other, even under linear atom-light interaction within each channel. We found that quantum correlations emerge in the phase unbroken regime and disappears after crossing the exceptional point. Our microscopic model considering quantum noise evolution produces results in good qualitative agreement with experimental observations. This work opens up a new direction of experimental quantum nonlinear optics using non-Hermitian systems, and demonstrates the viability of nonlinear coupling with linear systems by using atomic motion as feedback.