Revealing Genuine Optical-Path Entanglement

How can one detect entanglement between multiple optical paths sharing a single photon? We address this question by proposing a scalable protocol, which only uses local measurements where single photon detection is combined with small displacement operations. The resulting entanglement witness does not require postselection, nor assumptions about the photon number in each path. Furthermore, it guarantees that entanglement lies in a subspace with at most one photon per optical path and reveals genuinely multipartite entanglement. We demonstrate its scalability and resistance to loss by performing various experiments with two and three optical paths. We anticipate applications of our results for quantum network certification.

Figure 1

Proposal to build up 2D networks over long distances. (a) Networks made with neighboring nodes are made with $N$-path entangled states. (b) These local networks can be connected remotely by means of entanglement swapping operations resulting in a large scale network.

Figure 2

Three different setups used to test the proposed entanglement witness for two and three parties: (a) The heralded state can be tuned from maximally entangled to separable by the half-wave plate (HWP) ${\lambda }_E$ before the first polarizing beam splitter (PBS). The local oscillator is introduced at the other port of the PBS such that in each arm, the coherent state and the single photon have orthogonal polarization. The displacement operation is performed by rotating the HWPs at ${\lambda }_{D1}$ and ${\lambda }_{D2}$. (b) The single photon and coherent state are input earlier in the setup with orthogonal polarizations. The input loss can be varied to study the robustness of the witness. This setup can be easily modified, by adding a $30/70$ beam splitter and another (dashed) arm, allowing us to herald and probe a tripartite $W$ state.

Figure 3

Observed value for the bipartite entanglement witness (relatively to the PPT bound) as a function of the beam splitter ratio. Concretely, the half-wave plate ${\lambda }_E$ in Fig. 2 is rotated which changes the state from a maximally entangled to a separable state ($50/50–0/100$ splitting ratio, respectively). The blue band is obtained from a theoretical model, taking into account the setup’s global transmission, the characteristics of sources and gated detectors and the value for $|\alpha |\sim 0.83$ in the displacement operations.

Figure 4

Observed value for the bipartite entanglement witness (relatively to the PPT bound) as a function of loss. The total transmission consists of the photon coupling, transmission through the system, and detector efficiencies.