Signifying the nonlocality of NOON states using Einstein-Podolsky-Rosen steering inequalities

TL;DR

This paper develops EPR steering inequalities for NOON states to demonstrate their nonlocality and quantum coherence, providing a method to certify superpositions of mesoscopic quantum states.

Contribution

It introduces EPR steering signatures based on uncertainty relations for NOON states, enabling experimental certification of nonlocality and quantum coherence in these superpositions.

Findings

Violations of EPR steering inequalities confirm nonlocality of NOON states.

Signatures certify Nth order quantum coherence in superpositions.

Analysis of lossy scenarios suggests feasible experiments for N=2,3.

Abstract

We construct Einstein-Podolsky-Rosen (EPR) steering signatures for the nonlocality of the entangled superposition state described by $\frac{1}{\sqrt{2}}\{|N\rangle|0\rangle+|0\rangle|N\rangle\}$, called the two-mode NOON state. The signatures are a violation of an EPR steering inequality based on an uncertainty relation. The violation confirms an EPR steering between the two modes and involves certification of an inter-mode correlation for number, as well as quadrature phase amplitude measurements. We also explain how the signatures certify an $N$th order quantum coherence, so the system (for larger $N$) can be signified to be in a superposition of states distinct by a mesoscopic value of the two-mode quantum number difference. Finally, we examine the limitations imposed for lossy scenarios, discussing how experimental realisations may be possible for $N=2,3$.