Violation of Continuous Variable EPR Steering with Discrete Measurements

TL;DR

This paper derives entropic EPR steering inequalities for continuous variable systems using discrete measurements, demonstrating asymmetric and symmetric EPR steering in photon pairs from SPDC, and reducing experimental requirements.

Contribution

It introduces new entropic steering inequalities based on discrete measurements, enabling more practical tests of EPR steering in continuous variable systems.

Findings

Demonstrated EPR steering between photon positions and momenta.

Showed asymmetry can reduce experimental complexity.

Established symmetric EPR steering with a new inequality.

Abstract

In this Letter, we derive an entropic Einstein-Podolsky-Rosen (EPR) steering inequality for continuous variable (CV) 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 downconversion (SPDC). 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 downconverted photon pairs also exhibit symmetric EPR steering.