# Quantifying the mesoscopic nature of the Einstein-Podolsky-Rosen nonlocality

## TL;DR

This paper investigates mesoscopic EPR steering nonlocality in photonic and BEC systems, quantifying nonlocal effects involving large numbers of particles, and provides methods to estimate particle counts in entangled states.

## Contribution

It introduces a way to quantify mesoscopic EPR nonlocality and entanglement in large-particle systems, extending nonlocality analysis beyond microscopic scales.

## Key findings

- EPR nonlocality can be observed with up to 10^5 photons or tens of atoms.
- Variance criteria can estimate the minimum number of particles in entangled states.
- Methods are applicable to experimental data for large-scale quantum systems.

## Abstract

Evidence for Bell's nonlocality is so far mainly restricted to microscopic systems, where the elements of reality that are negated predetermine results of measurements to within one spin unit. Any observed nonlocal effect (or lack of classical predetermination) is then limited to no more than the difference of a single photon or electron being detected or not (at a given detector). In this paper, we analyze experiments that report Einstein-Podolsky-Rosen (EPR) steering form of nonlocality for mesoscopic photonic or Bose-Einstein condensate (BEC) systems. Using an EPR steering parameter, we show how the EPR nonlocalities involved can be quantified for four-mode states, to give evidence of nonlocal effects corresponding to a two-mode number difference of $10^{5}$ photons, or of several tens of atoms (at a given site). We also show how the variance criterion of Duan-Giedke-Cirac and Zoller for EPR entanglement can be used to determine a lower bound on the number of particles in a pure two-mode EPR entangled or steerable state, and apply to experiments.