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The dispersive interaction between a circular Rydberg atom and a superconducting millimeter-wave cavity creates an entangled quantum state of these two systems. Due to the long lifetime of the atomic levels and of the field, this correlation survives a long time after the atom has crossed the cavity mode. This situation is reminiscent of the EPR paradox, with non-local correlations between two subsystems. A quantum measurement performed on one part of this entangled state yields thus information on the other part.