For a complete and lucid discussion of quantum correlation, we introduced two new first-order correlation tensors defined as linear combinations of the general coherence tensors of the quantized fields and derived the associated coherence potentials governing the propagation of quantum correlation. On the basis of these quantum optical coherence tensors, we further introduced new concepts of scalar, vector and tensor densities and presented some related properties, such as conservation laws and the wave-particle duality for quantum correlation, which provide new insights into photon statistics and quantum correlation. 1. Introduction Fields interact with atoms in a fundamentally random or stochastic way. As a consequence, statistical interpretation of the outcome of most optical experiments becomes indispensable due to the fact that any measurement of light is accompanied by certain unavoidable fluctuations [1, 2]. Among various descriptions of the statistical properties of light, correlation between the fields at different space-time points, known as the correlation function, has long been recognized as the most fundamental physical quantity that plays a crucial role in photon correlations. The concept of optical correlation, first introduced by Wolf, has laid a foundation on which many important problems in classical statistical optics can be treated in a unified way. Also worth special mention is the quantum theory of optical coherence created by Glauber [3–5], who took a quantum electrodynamics approach to the problems of photon statistics. Because of its theoretical and practical importance, coherence theory and quantum optics have developed into a challenging multifarious field of research. In quantum optics, detection of photons based on the absorption of photons via the photoelectric effect constitutes the basis of the measurements of the optical field. Photon statistics and quantum correlations have been studied extensively. However, the discussions in most of papers are restricted to the correlations between the same kinds of fields (either between electric fields themselves or between magnetic fields themselves) at different space-time points, and the mixed correlation between electric field and magnetic field, introduced by Mehta and Wolf [6], seems to have received less attention in spite of its importance. Although the quantum theory for the correlations between the same kind of fields has already been established and is indeed informative, this alone cannot constitute a self-consistent theoretical framework for the full description of the
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