MZI: U=B† diag(1,eⁱφ) B; P₀=η(T²+R²+2TR cosφ), P₁=2ηTR(1−cosφ), P∅=1−η. HOM: P₁₁=T²+R²−2TRμ, P₂₀=P₀₂=TR(1+μ); R=1−T, μ=m e⁻δ².
Assumptions and limits
- Ideal linear optics in two spatial modes. T is power transmissivity, with transmission amplitude √T. Coupler phases follow B=[[√T,−√R],[√R,√T]]; the MZI uses its inverse as the second coupler.
- The MZI starts in |10⟩ and preserves phase coherence. The shared output efficiency η combines equal optical loss and detector inefficiency. No detection remains in the displayed probability total; no dark counts or background photons.
- HOM starts with exactly one photon in each input and assumes lossless propagation and ideal photon-number-resolving detection. Output numbers are occupations of two modes, not two logical qubits.
- HOM assumes pure Gaussian temporal envelopes with equal intensity standard deviation σₜ and a factorizable remaining mode overlap m. δ=τ/(2σₜ); μ is squared overlap. Delay has no physical duration until σₜ is specified.
- Geometry is an optical circuit schematic, not a crystal lattice or calibrated chip layout. All probabilities are analytic model predictions; neither hardware fidelities nor measured counts are inferred. Photonic systems are not universally room-temperature devices.
Sources · 4 references
