Detection of non-Gaussian quantum correlations through measurement-after-interaction protocols

Abstract

Additional state evolutions performed before measurement, also called measurement-after-interactions (MAI) protocols, have shown a great potential for increasing the sensitivity of metrological scenarios. Here, we go beyond this result and show that MAI techniques can significantly enhance the detection capability of witnesses for quantum correlations. In particular, we show the possibility of detecting Einstein-Podolsky-Rosen steering and mode entanglement of non-Gaussian states from linear measurements only. Moreover, we show that such approach allows for a significantly higher noise robustness.

Figures (6)

• Figure 1: Illustration a phase estimation protocol assisted by an MAI technique in the framework of EPR paradox. Alice assists Bob in his metrological task by communicating her measurement choice and associated results. Based on this information, Bob will either estimate the generator $G$ or the phase $\theta$ through an MAI technique. In the latter, the probe state will undergo an evolution $U$ before being detected. A violation of complementarity between the estimation uncertainty of $\theta$ and $G$ indicates EPR steering between Alice and Bob.
• Figure 2: Comparison between steering criteria and average sensitivities as a function of $\mu$, for a split spin squeezed states with $N=20$. (a) maximum violation of the steering criteria showing the hierarchy $\delta^R_{\text{L}}\leq \delta^R_{\text{MAI}} \leq \delta^F$. (b) first term in the criteria, showing the average sensitivities $(\chi^{-2}_{\text{L}})^{B|A}[\mathcal{A},G,M_{\text{L}},Y] \leq (\chi^{-2}_{\text{MAI}})^{B|A}[\mathcal{A},G,M_{\text{MAI}},Y] \leq F^{B|A}[\mathcal{A},G,Y]$. (c) for $\mu=0.4$, Wigner functions after encoding and MAI interaction using Bob's conditional states $\rho^B_{(l_A=5,N_A=10|Y)}$.
• Figure 3: Robustness to detection noise. Maximum violation of the steering criteria $\delta^R_{\text{MAI}},\delta^R_{\text{L}}$ as a function of the standard derivation of detection noise $\sigma$ for squeezing $r=0.5$. Noise robustness increases as the squeezing $r_2$ in MAI technique increases.
• Figure 4: Mode entanglement in a split spin squeezed state with $N=20$ atoms. Comparison of the violation of Giovannetti's criterion under the typical and MAI protocols as a function of $\mu$.
• Figure 5: For a split spin states with atoms $N=20$, we compare the squeezing coefficients $\delta^R_{\text{MAI}}$ when the MAI unitary operator is $U_{\text{MAI}}=e^{i\frac{\mu_2}{2} \left( S_z^B \right)^2}$ (yellow line) and $U_{\text{MAI}}(\vec{n}_{\text{opt}})=e^{i\frac{\mu_2}{2} ( S_{\vec{n}_{\text{opt}} }^B )^2}$ with the optimal rotation axis $\vec{n}_{\text{opt}}$ (brown line).