Realization of the Einstein-Podolsky-Rosen paradox for continuous variables.

The Einstein-Podolsky-Rosen (EPR) paradox is demonstrated experimentally for continuous variables by employing a nondegenerate optical parametric amplifier (NOPA). Such a system is analogous to and under some ideal conditions is in one-to-one correspondence with the original system discussed by EPR. In particular, the quadrature-phase amplitudes for a signal beam are inferred in turn from those of a spatially separated but strongly correlated idler beam, where these optical amplitudes are analogous to canonical position and momentum variables. The variances for the two inferences are measured and their product is observed to be below the limit of unity associated with the Heisenberg uncertainty relation, in apparent contradiction with quantum mechanics according to the argument of EPR. The smallest product of inference variances achieved in the experiment is (0.70 40.01). Various other types of quantum noise for this system are also investigated, and a theory of a narrowband NOPA is presented with losses included. A comparison between experiment and this theory shows relatively good agreement. The question of a local hidden-variables description of the system is discussed.