Full range of states achievable via path-identity constructions

Determine the full range of quantum states achievable through path-identity constructions by characterizing exactly which entangled states can be generated using path-identity-based photonic setups, in which photons from independent sources become entangled without direct interaction, pre-shared entanglement, or Bell-state measurements.

Background

The paper demonstrates that path identity—making photon emission origins indistinguishable—can generate multipartite, high-dimensional, and logical entanglement between spatially separated nodes without direct interaction, pre-shared entanglement, or Bell-state measurements. Using the automated design tool PyTheus, the authors present explicit configurations that produce GHZ and W states, high-dimensional Schmidt-rank vector states, and logical entanglement (including hybrid logical–physical forms).

While these examples illustrate the power and generality of path-identity techniques, the authors explicitly note that a comprehensive characterization of all states achievable by such constructions is not yet known. Establishing this characterization would clarify the ultimate expressive capacity of path-identity designs within quantum networking and distributed quantum information processing.