Demonstrating Continuous Variable EPR Steering in spite of Finite Experimental Capabilities using Fano Steering Bounds

TL;DR

This paper introduces a method to demonstrate continuous-variable EPR steering using Fano bounds, effectively addressing experimental limitations like finite detector size and incomplete sampling, validated with photon pair data.

Contribution

Develops a modified Fano inequality for discrete measurements of continuous variables to demonstrate EPR steering without full distribution characterization.

Findings

Method successfully demonstrates EPR steering with experimental data.

Effective in mitigating effects of finite detector size and sampling issues.

Applicable to practical quantum optics experiments.

Abstract

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.