Tailoring entanglement with a symmetry: Anomalous ghost diffraction

Coherence is a fundamental property of light. Recent years have witnessed a growing interest in coherence structuring, yielding a new type of partially coherent source with spatially tailored nonuniform correlations. However, the routine way of producing entangled photons via parametric down-conversion is to use a highly coherent laser source to pump nonlinear crystals. Here, we present a new strategy of exploiting such nonuniformly partially coherent sources to excite parametric down-conversion and thus endow the generated entanglement with a tailored and unusual spatial symmetry. To reveal the spatially varying degree of entanglement, we demonstrate the observation of an unusual Einstein-Podolsky-Rosen (EPR) correlation by transferring the circular structure of the coherence of the pump beam onto that of down-converted photons. For this, we observe both anomalous ghost diffraction and normal ghost images to examine the EPR-type inequalities and showcase the transition from nonentanglement to entanglement. Our work suggests that coherence structuring can offer a new dimension to generate and control quantum entanglement.