Demonstration of Einstein-Podolsky-Rosen Steering Using Single-Photon Path Entanglement and Displacement-Based Detection

We demonstrate the violation of an Einstein-Podolsky-Rosen steering inequality developed for single-photon path entanglement with displacement-based detection. We use a high-rate source of heralded single-photon path-entangled states, combined with high-efficiency superconducting-based detectors, in a scheme that is free of any postselection and thus immune to the detection loophole. This result conclusively demonstrates single-photon entanglement in a one-sided device-independent scenario, and opens the way towards implementations of device-independent quantum technologies within the paradigm of path entanglement.

Figure 1

Conceptual view of our steering experiment. Single-photon path entanglement is created by splitting a single photon on a beam splitter. Entanglement between the output modes of the beam splitter is certified in a one-sided DI scenario, via violation of a steering inequality. Alice’s device is untrusted (black box), while Bob’s device implements characterized (hence trusted) displacement-based detections where the displacement $D(\alpha )$ is a function of a measurement input $y$.

Figure 2

Experimental setup. A heralding single-photon source is coupled into fiber and incident on a fiber BS, generating heralded entanglement, while local oscillator states, switched by an EOM, are coupled into the same BS with orthogonal polarization. Weak displacements, $\widehat{\mathcal{D}}(\alpha )$, $\widehat{\mathcal{D}}(\beta )$, are performed in an all-fiber configuration (inset) followed by single-photon detectors that constitute the displacement-based detection. See the main text for details and notation.

Figure 3

Observed joint probabilities $p(a,b)$ for click and no-click events of Alice and Bob as functions of the relative phase between displacements (red points). A fit (blue lines) is used to identify which points (arrows) are used to compute the steering value. Error bars (sometimes smaller than the points) correspond to one standard deviation.