Fig. 3: Disappearance and revival of EPR steering in noisy channel.
From: Sudden death and revival of Gaussian Einstein–Podolsky–Rosen steering in noisy channels
a, b Steering parameters quantified by Eqs. (4) and (5) in a noisy channel where the variance of the excess noise is taken as five times of vacuum noise, respectively. Black dash and solid curves are the theoretical predictions of \({{\mathcal{G}}}^{{B}_{N}\to A}\) and \({{\mathcal{G}}}^{A\to {B}_{N}}\), respectively. Region I, two-way steering; region II, one-way steering; region III, no steering. Red dash and solid curves are the theoretical predictions of \({{\mathcal{G}}}^{{B}_{R}\to A}\) and \({{\mathcal{G}}}^{A\to {B}_{R}}\) after steering revival, respectively. The blue dash and solid curves are the theoretical predictions of \({{\mathcal{G}}}^{{B}_{L}\to A}\) and \({{\mathcal{G}}}^{A\to {B}_{L}}\) in a pure lossy but noiseless channel. c, d Steering parameters quantified by Eqs. (4) and (5) in a transmission efficiency fixed (ηN = 0.6) noisy channel with different noise levels. Black dash and solid curves are theoretical predictions of \({{\mathcal{G}}}^{{B}_{N}\to A}\) and \({{\mathcal{G}}}^{A\to {B}_{N}}\) as a function of the excess noise in the unit of shot noise level. Red dash and solid curves are the theoretical predictions of \({{\mathcal{G}}}^{{B}_{R}\to A}\) and \({{\mathcal{G}}}^{A\to {B}_{R}}\) after steering revival, respectively. The inset figure shows the detailed theoretical predictions of \({{\mathcal{G}}}^{{B}_{R}\to A}\) and \({{\mathcal{G}}}^{A\to {B}_{R}}\) when the excess noise is relatively low. Error bars of experimental data represent ±1 standard deviation and are obtained based on the statistics of the measured data.
