Not yet reviewed by Pith; the record is open.

Optical coherence encodes information about the correlations of the electromagnetic field. In combination with quantum optical approaches, it allows for the study of the correlations between photons. Since the pioneering papers of Glauber, studies of optical coherence have facilitated many fundamental insights into non-classical signatures of light emission processes, with wide applicability in modern quantum technologies. However, when it comes to the photon up-conversion process of high-order harmonic generation the description has focused on semi-classical methods for decades. In this work, we overcome this limitation and establish a quantum optical theory of field correlations for the process of high harmonic generation (HHG). In effect, we introduce the notion of optical coherence at the intersection of quantum optics and strong laser-driven processes, and obtain the harmonic field correlation functions. In particular, we focus on the first and second order field correlation, which allow to understand the origin of the classical properties of the HHG spectrum, and its departure into the quantum regime. Further, we develop the theory for two-time intensity correlation functions of the harmonic field, and demonstrate the onset of anti-bunching signatures in HHG. We study the correlation functions in the regime of a single, few and many emitters in atomic HHG, showing the transition from quantum to classical signatures in the correlations. Since the theory is generic, it can be extended to multi-time correlation functions of any order, and allows to consider the interaction of light with arbitrary material systems.