Revealing Hidden Einstein-Podolsky-Rosen Nonlocality

Steering is a form of quantum nonlocality that is intimately related to the famous Einstein-Podolsky-Rosen (EPR) paradox that ignited the ongoing discussion of quantum correlations. Within the hierarchy of nonlocal correlations appearing in nature, EPR steering occupies an intermediate position between Bell nonlocality and entanglement. In continuous variable systems, EPR steering correlations have been observed by violation of Reid’s EPR inequality, which is based on inferred variances of complementary observables. Here we propose and experimentally test a new criterion based on entropy functions, and show that it is more powerful than the variance inequality for identifying EPR steering. Using the entropic criterion our experimental results show EPR steering, while the variance criterion does not. Our results open up the possibility of observing this type of nonlocality in a wider variety of quantum states.

Figure 1

Experimental setup. SPDC in a BBO crystal produces spatially entangled photon pairs ($\lambda =884\mathrm{nm}$). A microscope slide is used to produce a first-order Hermite Gaussian beam, which is focused at the crystal face with a cylindrical lens. Lenses ($f=100\mathrm{mm}$) are used to map the momentum distribution at the crystal face onto the output planes, where transmission masks with a Gaussian intensity profile are placed. The figure shows the setup for $p$ measurements. Diagrams for the lens systems used for $x$ and $p$ measurements are shown in the bottom left. Here $f_1=150\mathrm{mm}$, $f_2=50\mathrm{mm}$ and $f_3=250\mathrm{mm}$. The horizontal slit detection apertures are mounted directly onto Detectors $D_A$ and $D_B$ (not shown for clarity), and are scanned in the vertical direction.

Figure 2

Coincidence counts for $x$ and $p$ measurements used to calculate the probability distributions $\mathcal{P}(x_A,x_B)$ and $\mathcal{P}(p_A,p_B)$.