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Conference on Lasers and Electro-Optics

EPR inequality and Heisenberg uncertainty principle

Milena D’Angelo, Morton H. Rubin, Yanhua H. Shih

Published Jan 1, 2004• 1 citation
Publisher

Abstract

We prove a non-classicality condition which allows distinguishing entanglement from classical correlation in continuous variables, for two photons/particles systems. This implies that entanglement can overcome the limitations imposed by the uncertainty principle on factorable states.
DOI
10.1364/iqec.2004.ituj6

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We report a quantum interference and imaging experiment which allows identifying the entanglement in momentum and position variables of a two-photon system. The measurements show indeed that the uncertainties in the sum of momenta and in the difference of positions of the entangled two-photon satisfy both EPR inequalities $\ensuremath{\Delta}({k}_{1}+{k}_{2})<\mathrm{min}(\ensuremath{\Delta}{k}_{1},\ensuremath{\Delta}{k}_{2})$ and $\ensuremath{\Delta}({x}_{1}\ensuremath{-}{x}_{2})<\mathrm{min}(\ensuremath{\Delta}{x}_{1},\ensuremath{\Delta}{x}_{2})$. These two inequalities, together, represent a nonclassicality condition. Our measurements provide a direct way to distinguish between quantum entanglement and classical correlation in continuous variables for systems of pairs of photons.
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An entangled EPR two-particle system is characterized by Δ(p 1 + p 2) = 0 and Δ(x 1 - x 2) = 0, simultaneously, with the momentum and position of each individual particle completely undefined. Statistically, however, the uncertainty of the correlation measurements on the two individual particles must obey Δ(p1 + p 2) > Δp 1,2 and Δ(x 1 - x 2) > Δx 1,2. While one sees the measurements of p 1 + p 2 and x 1 - x 2 of the two individual particles satisfying the EPR δ-function, and believes the classical statistical inequality, one might easily be trapped into concluding either there is a violation of the uncertainty principle or there exists action-at-a-distance. Through the analysis of three typical EPR experiments, we show that the measurement of p 1 + p 2 and x 1 - x 2 for an entangled system can indeed violate the classical statistical inequality. Based on the experimental results, we emphasize, again, the surprising physics of quantum coherent two-particle superposition. Although questions regarding fundamental issues of quantum theory still exist, quantum entanglement has brought us a novel concept in non-local timing and positioning measurements with ultra-high accuracy, even beyond the classical limit.