Connecting heterogeneous quantum networks by hybrid entanglement swapping

Abstract

Recent advances in quantum technologies are rapidly stimulating the building of quantum networks. With the parallel development of multiple physical platforms and different types of encodings, a challenge for present and future networks is to uphold a heterogeneous structure for full functionality and therefore support modular systems that are not necessarily compatible with one another. Central to this endeavor is the capability to distribute and interconnect optical entangled states relying on different discrete and continuous quantum variables. Here, we report an entanglement swapping protocol connecting such entangled states. We generate single-photon entanglement and hybrid entanglement between particle- and wave-like optical qubits and then demonstrate the heralded creation of hybrid entanglement at a distance by using a specific Bell-state measurement. This ability opens up the prospect of connecting heterogeneous nodes of a network, with the promise of increased integration and novel functionalities.

Fig. 1. A heterogeneous quantum network linked by entanglement swapping.

A DV node, on the left, establishes a link to a hybrid node, on the right, via a swapping protocol implemented by a Bell-state measurement (BSM) at an intermediate station. Hybrid CV-DV entanglement is created between two modes that never interacted. The resulting entangled state is available to perform subsequent remote state preparation, to enable teleportation-based encoding conversion, or to connect disparate physical platforms at longer distances.

Fig. 2. Experimental setup.

The gray panels outline the nonlinear sources and operations, i.e., optical parametric oscillators and heralding measurements. CV states are produced via a single-mode squeezer (OPO I), while DV states are generated by a two-mode squeezer (OPO II). The sources are used at different times to generate DV single-photon entanglement between modes A and B first and hybrid DV-CV entanglement between modes C and D afterward. The matrices show the measured entangled states: single-photon entanglement heralded by superconducting nanowire single-photon detector (SNSPD) α (bottom) and hybrid entanglement heralded by SNSPD β (top, Wigner representation of the reduced states). To prepare for entanglement swapping, a delay line holds off the state in mode B to enable the temporal matching of one DV mode from each of the two initial states. These modes are mixed at the BSM station (light brown panel), where a combination of a detection event on SNSPD γ and a quadrature measurement via homodyne detection (HD) is performed. Upon success, hybrid entanglement is heralded between modes A and D where high-efficiency homodyne detections are used for full two-mode quantum state tomography.

Fig. 3. Entanglement swapping results.

Tomographic measurements of the initial entangled states are given on the left, with DV-DV entanglement at the top and hybrid CV-DV entanglement at the bottom. The right side provides the measurement of the output state when the BSM heralds entanglement swapping and, for reference, when no BSM is implemented (see the Supplementary Materials for more specific comparison). All states are displayed using two representations, a hybrid density-Wigner plot and a density matrix giving the reconstructed state projected in the relevant basis (vacuum–single-photon {∣0⟩, ∣1⟩} for DV and coherent-state superpositions {∣cat₊⟩, ∣cat₋⟩} for CV). The number of tomographic samples for each state reconstruction is 600,000; 200,000; 7800; and 200,000 respectively. For simplicity, only the real part of the density matrices is shown, as the imaginary part consists of near-zero elements of magnitude smaller than 1%. The input states coincide with those featured in Fig. 2.

Fig. 4. Swapping for remote hybrid entanglement distribution.

The expected entanglement negativity after swapping of the experimental initial resources is evaluated as a function of the channel loss (considered symmetric on the two channels). The black solid line corresponds to an ideal BSM with vanishing reflectivity R and quadrature conditioning window Δ, while the green line corresponds to the implemented case (R = 10% and Δ equal to the vacuum shot noise). The gray dotted line corresponds to a BSM without homodyne conditioning. The effect of dark counts is presented by the green dashed line (1% of total events). The white point gives the measured output negativity, in good agreement with the simulation. As a reference, the blue line shows the negativity for direct propagation. The inset provides the same plots but starting from maximally entangled input states and without dark counts.