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Summary form only given. Optical system which display quantum entanglement properties in the spatial domain are of great interest for applications, since the amount of information that can be manipulated and processed in parallel exploiting quantum correlation effects increase substantially. In this paper, we consider the field generated through the process of frequency down-conversion in a travelling wave optical parametric amplifier. We present new results showing that the two images are locally correlated, not only with respect to intensity fluctuations, but also to phase fluctuations.