Automated discovery of high-dimensional multipartite entanglement with photons that never interacted

TL;DR

Path-identity entanglement enables correlations between remote quantum processors without direct photon interaction or pre-shared entanglement, offering a distinct resource for distributed quantum information. The authors leverage path identity and automated design tools (PyTheus) to automatically discover a broad family of schemes that generate multipartite, high-dimensional, and even encoded logical entanglement across separated nodes, including GHZ, W, SRV states, and various quantum-error-correcting codes. These results demonstrate that non-interacting indistinguishable emission processes can serve as a powerful resource for distributed quantum networks and fault-tolerant communication. The work also showcases AI-assisted hypothesis generation (AI-Mandel) coupled to automated photonic design as a route to rapidly explore large design spaces in quantum optics.

Abstract

Quantum entanglement across spatially separated network nodes is conventionally established through the distribution of photons from a common source or via entanglement swapping that relies on Bell-state measurements and pre-shared entanglement. Path identity, where the emission origins of photons from different sources are made indistinguishable, offers an alternative route. We show that this mechanism enables complex multipartite, high-dimensional, and even logical entanglement between remote nodes whose photons never interacted. Our schemes require neither direct photon interaction, pre-shared entanglement, nor Bell-state measurements, highlighting a distinct resource for distributed quantum communication and computation. All of the solutions were discovered automatically using highly efficient computational design tools, indicating the potential for scientific inspiration from computational algorithms.

Figures (10)

• Figure 1: Methods for establishing entanglement across separated locations.(a). We consider three stations: a shared system and two distant sites A and B. (b). The simplest way is to generate entanglement at a common source (for example a Bell state $|\Phi^+\rangle$, as indicated in the white rectangle) and then sent to A and B. This scenario was first described by Einstein, Podolsky, and Rosen in 1935 einstein1935can and later demonstrated by Freedman and Clauser in 1972 freedman1972experimental. (c). Entanglement swapping allows photons at A and B to become entangled without interacting before. Two pre-shared Bell pairs $|\Phi^+\rangle$ and a Bell state measurement (BSM) at the central node are used zukowski1993event, and this was demonstrated in 1998 pan1998experimental. (d). Path identity generates entanglement between photons that never interacted, without Bell-state measurements and pre-shared entanglement krenn2017entanglementruiz2023digital. This was discovered by PyTheus ruiz2023digital and experimentally demonstrated in 2024 wang2024entangling. The photon sources produce photon pairs or product states, indicated by the symbol $\otimes$. (e). In the present work, complex multipartite and high-dimensional entangled states are established across separated locations without direct interaction, pre-shared entanglement, or Bell state measurements.
• Figure 2: Multi-photon GHZ states with photons that never interacted at two separated locations.(a) The simplest case: a two-photon Bell state, which can be considered as the two-photon instance of a GHZ state. The remote photons in paths 0 and 1 are at locations $A$ and $B$, while ancillary photons are detected in paths $a_{1},a_{2}$. (b–d) Extension to four-, six-, and eight-photon GHZ states. Neither pre-shared entanglement nor Bell-state measurements are required. Photon pairs are generated in nonlinear crystals (for example, the blue-blue rectangle denotes a photon pair in the state $|00\rangle$). Photons at sites $A$ and $B$ become entangled without ever interacting.
• Figure 3: Multi-photon W states with photons that never interacted at separated locations.(a) A two-photon Bell state $|\Psi^+\rangle$, can be considered as the two-photon case of a W state. (b–d) Four-, six-, and eight-photon W states distributed across two, three, and four locations. Photons at different sites that never met become entangled.
• Figure 4: SRV(4,2,2) state distributed across three spatially separated locations with photons in paths 0--2 that never interacted. Basis states are color-coded: $|3\rangle$ (yellow), $|2\rangle$ (green), $|1\rangle$ (red), and $|0\rangle$ (blue). Ancillary photons in paths $a_{1}$--$a_{5}$ are prepared in $|0\rangle$.
• Figure 5: Logical Bell state with the error detection code $[[4,1,2]]$ encoding. Each logical qubit is encoded into four physical qubits (photons), located at sites $A$ (paths 0–3) and $B$ (paths 4–7). The logical Bell state is established between the two sites even though photons at $A$ and $B$ never met. No direct interaction, pre-shared entanglement, or Bell-state measurements are required.