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Summary form only given. Entangled states of multi-particle systems are arguably the quintessential feature of quantum mechanics. In addition to their central role in discussions of nonlocal quantum correlations, they form the basis of quantum information, and enable such phenomena as quantum cryptography, quantum dense coding, teleportation, and quantum computation. Yet surprisingly, to date only a limited class of entangled states has ever been produced. Via the process of spontaneous parametric downconversion in a pair of nonlinear crystals, it is now possible to produce, with high-efficiency, pairs of photons entangled in their polarization degree of freedom. Further, we can control both the extent of entanglement and the purity of the state.