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

Abstract

We construct Einstein-Podolsky-Rosen (EPR) steering signatures for the nonlocality of the entangled superposition state described by $\frac{1}{\sqrt{2}}\{|N⟩|0⟩+|0⟩|N⟩\}$, 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 $N=2,3$.

16 pages (9 pages text and 7 pages Appendix) with 2 Figures

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• NOON-state interference in the frequency domain
• Testing macroscopic local realism using cat-states and Bell inequalities in time
• Einstein-Podolsky-Rosen steering, depth of steering and planar spin squeezing in two-mode Bose-Einstein condensates
• Macroscopic delayed-choice and retrocausality: quantum eraser, Leggett-Garg and dimension witness tests with cat states
• Certification of non-Gaussian Einstein-Podolsky-Rosen Steering
• Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
• Generation of N00N-like interferences with two thermal light sources