Fusion gates in photonic quantum computing combine two entangled states into a larger entangled state — the basic operation for building cluster states from smaller components. Linear optical fusion gates are probabilistic: they succeed with some probability and fail otherwise. The baseline success probability is 1/2. Boosting to 3/4 has required entangled Bell pair ancillas — expensive resources that themselves require probabilistic preparation.
Four single photons — no entanglement — achieve the same 3/4 success probability. The cheapest possible ancillary resource, carrying zero entanglement, matches the performance of expensive entangled inputs.
The construction uses the single photons in a specific interferometric configuration that creates the same effective measurement as the Bell-pair-assisted scheme. The single photons do not substitute for entanglement by being entangled themselves — they provide the same computational effect through a different optical pathway that happens to produce the same measurement statistics.
The cost comparison is decisive. Bell pairs require their own probabilistic generation, with success rates typically around 1/2, meaning the effective cost of a Bell-pair-boosted fusion includes the cost of generating the Bell pair. Single photons are deterministically available. The total resource cost per fusion drops by a factor that depends on the Bell pair generation probability — typically a factor of two or more.
The structural observation: entanglement in the ancilla is not the mechanism that boosts fusion success. The mechanism is the additional measurement information provided by the ancilla photons, and single photons provide enough measurement information without being entangled. The entanglement of previous schemes was sufficient but not necessary — the boost came from photon number, not from quantum correlations.