Demonstrating Continuous-Variable Einstein-Podolsky-Rosen Steering With A Finite Number Of Measurements

Here, we discuss the development of a new inequality in information theory; a Fano inequality suitable for continuous variables. With this inequality, we show how one can demonstrate Einstein-Podolsky-Rosen (EPR) steering in the position-momentum statistics of entangled photon pairs from spontaneous parametric downconversion (SPDC). More importantly, we show how with sufficiently strong position and momentum correlations, we can demonstrate continuous-variable EPR steering without having to assume the photo-detectors have access to the entire joint intensity distribution. Moreover, we demonstrate this experimentally with the position and momentum statistics of entangled photon pairs in SPDC.