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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Demonstrating continuous-variable Einstein-Podolsky-Rosen steering with a finite number of measurements

James Schneeloch, Samuel H. Knarr, Gregory A. Howland, John C. Howell

Published May 21, 2015• 0 citations
Publisher

Abstract

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 down-conversion (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.

DOI
10.1117/12.2177296

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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 down-conversion (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.
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.
In this Letter, we derive an entropic Einstein-Podolsky-Rosen (EPR) steering inequality for continuous-variable systems using only experimentally measured discrete probability distributions and details of the measurement apparatus. We use this inequality to witness EPR steering between the positions and momenta of photon pairs generated in spontaneous parametric down-conversion. We examine the asymmetry between parties in this inequality, and show that this asymmetry can be used to reduce the technical requirements of experimental setups intended to demonstrate the EPR paradox. Furthermore, we develop a more stringent steering inequality that is symmetric between parties, and use it to show that the down-converted photon pairs also exhibit symmetric EPR steering.
Steering is a form of quantum nonlocality that is intimately related to the famous Einstein-Podolsky-Rosen (EPR) paradox that ignited the ongoing discussion of quantum correlations. Within the hierarchy of nonlocal correlations appearing in nature, EPR steering occupies an intermediate position between Bell nonlocality and entanglement. In continuous variable systems, EPR steering correlations have been observed by violation of Reid's EPR inequality, which is based on inferred variances of complementary observables. Here we propose and experimentally test a new criterion based on entropy functions, and show that it is more powerful than the variance inequality for identifying EPR steering. Using the entropic criterion our experimental results show EPR steering, while the variance criterion does not. Our results open up the possibility of observing this type of nonlocality in a wider variety of quantum states.
Due to practical reasons, experimental and theoretical continuous-variable (CV) quantum information (QI) has been heavily based on Gaussian states. Nevertheless, many CV-QI protocols require the use of non-Gaussian states and operations. Here, we show that the Einstein-Podolsky-Rosen-steering inequality can be used to obtain a practical witness for the generation of pure bipartite non-Gaussian states. While the scenario requires pure states, we show its broad relevance by reporting the experimental observation of the non-Gaussianity of the CV two-photon state generated in the process of spontaneous parametric down-conversion (SPDC). The observed non-Gaussianity is due only to the intrinsic phase-matching conditions of SPDC.
Einstein-Podolsky-Rosen (EPR) entanglement introduced in 1935 deals with two particles that are entangled in their positions and momenta. Here we report the first experimental demonstration of EPR position-momentum entanglement of narrow-band photon pairs generated from cold atoms. By using two-photon quantum ghost imaging and ghost interference, we demonstrate explicitly that the narrow-band photon pairs violate the separability criterion, confirming EPR entanglement. We further demonstrate continuous variable EPR steering for positions and momenta of the two photons. Our new source of EPR-entangled narrow-band photons is expected to play an essential role in spatially multiplexed quantum information processing, such as, storage of quantum correlated images, quantum interface involving hyperentangled photons, etc.