Characterize distinguishability transformation by fusion operations

Characterize how different photonic fusion operations transform the distinguishability content of the surviving heralded state, beyond their effects on measurement outcomes and effective distinguishability-induced errors.

Background

The paper distinguishes partial distinguishability effects that appear as effective measurement errors from the transformation of the distinguishability properties of the unmeasured photons that remain after a successful fusion event. Although the former has been studied extensively, the authors identify the latter as comparatively underexplored.

This problem is central to the paper’s motivation: fusion operations may alter the quality of heralded entangled states in protocol-, heralding-pattern-, and error-model-dependent ways. A fuller characterization is relevant for modeling repeated fusion operations in large-scale photonic quantum computation.

References

However, they do not generally capture the effect that a fusion operation may have on the distinguishability properties of the remaining heralded state. Consequently, while distinguishability-induced measurement errors have received considerable attention, comparatively little is known about how different fusion operations transform the distinguishability content of the surviving state itself.

— Photonic fusion operations transform partial distinguishability  (2609.01019 - Hoven et al., 1 Sep 2026) in Section 2.1, “Photonic fusions”

This gives rise to the hypothesis that the size of the resource state has a smaller impact on distinguishability propagation compared to the error model.

— Photonic fusion operations transform partial distinguishability  (2609.01019 - Hoven et al., 1 Sep 2026) in Section 3.2, “Distinguishability propagation in an FBQC-inspired fusion sequence”