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In this talk, the quantum state of an electromagnetic field in contact with dielectric matter at zero temperature is described. I consider the reduced density matrix of the field, which is entangled with the dielectric and show that it is not thermal. I describe the cutoff dependence of the field entropy and derive formulas for the part of the entanglement entropy associated with the distance between two dispersive objects, in a philosophy similar to the one used in Casimir physics. Finally we describe the distance dependence of the second Renyi entropy of two objects which are far apart.
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