Beyond the Heisenberg uncertainty

Abstract

Following Einstein, Podolsky, and Rosen (EPR) original argument, we derive a pair of inequalities for the uncertainties in the sum of the momenta and in the difference of the positions of an entangled two-particle system. We prove that only entangled systems can satisfy both EPR-inequalities, in violation of the limits imposed by classical statistics. We propose an operational approach that allows applying the EPR inequalities to two-photon systems, as well. In particular, we demonstrate a scheme that allows implementing the EPR gedanken-experiment and verifying the EPR inequalities on systems of pairs of photons. We report the experimental results obtained in this kind of quantum interference and imaging experiment: SPDC two-photon system satisfies both EPR inequalities. The experimental verification of the EPR inequalities represents a practical way to experimentally distinguish entanglement from classical correlation in momentum and/or position variables for systems of two particles/photons. We emphasize the practical consequences of the EPR inequalities: only entanglement allows one to go beyond the limitations imposed by Heisenberg uncertainty on systems of classically correlated particles/photons. In this context we review a recent experiment of two-photon diffraction and quantum lithography.