Number-phase entanglement and Einstein-Podolsky-Rosen steering

Abstract

We use the uncertainty relation between the operators associated with the total number of particles and with the relative phase of two bosonic modes to construct entanglement and Einstein-Podolsky-Rosen steering criteria. These can be tested experimentally in a variety of systems, such as optical fields, Bose-Einstein condensates, and mechanical oscillators. While known entanglement criteria involving the phase observable typically require us to perform interference measurements by recombining the two systems, our criteria can be tested through local measurements at two spatially distinct positions to investigate the nonlocal nature of quantum correlations. We present simple examples where our criteria are violated and show their robustness to noise. Apart from being useful for state characterization, they might find application in quantum information protocols, for example, based on number-phase teleportation.

Propagation-induced entanglement revival

“…The fitting is based on the noise model described in Eq. (25). ∆(l s |l i ; z) to be 0.72 in our experiments.…”

Propagation-induced revival of entanglement in the angle-OAM bases

“…In this article, we explore entanglement of down-converted photons in the continuous-variable bases of angle and OAM. We certify entanglement through EPR correlation measurements ( 14 – 17 , 22 , 44 ) and demonstrate that the entanglement of down-converted photons in the angle-OAM bases exhibits a different behavior than the entanglement in the position-momentum bases. Just as in the case of position-momentum bases, initially, the angle-OAM entanglement decays with propagation, but as the photons continue to travel further away from the source, the entanglement in the angle-OAM bases comes back.…”

Magnon-magnon entanglement and its detection in a microwave cavity

“…A highly relevant concept to continuous variable entanglement is the Bell type nonlocal correlations known as Einstein, Podolsky and Rosen (EPR) nonlocality. In the present case, the EPR nonlocality can be quantified by the following EPR function [18]…”

“…The Var ψ (V ) is the variance of an Hermitian operator V with respect to the state |ψ . The uncertainty relation ∆(ψ) ≥ 1 is known to hold for any given bipartite separable state |ψ [18]. Therefore, any violation of this inequality is an indication of the state |ψ being nonlocal and indeed a bipartite entangled state.…”