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Frontiers in Optics

Witnessing Continuous Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements

James Schneeloch, P. Ben Dixon, Gregory A. Howland, Curtis J. Broadbent, John C. Howell

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We create a stronger EPR-steering inequality for continuous variables using entropic uncertainty and discrete measurements. We explore the asymmetry in this inequality and develop a new symmetric inequality. We also violate these inequalities in experiment.
DOI
10.1364/fio.2013.fw5d.4

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We show how one can demonstrate continuous-variable Einstein–Podolsky–Rosen (EPR) steering without needing to characterize entire measurement probability distributions. To do this, we develop a modified Fano inequality useful for discrete measurements of continuous variables and use it to bound the conditional uncertainties in continuous-variable entropic EPR-steering inequalities. With these bounds, we show how one can hedge against experimental limitations including a finite detector size, dead space between pixels, and any such factors that impose an incomplete sampling of the true measurement probability distribution. Furthermore, we use experimental data from the position and momentum statistics of entangled photon pairs in parametric downconversion to show that this method is sufficiently sensitive for practical use.
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