Lossy Fock boson sampling probabilities are finite Fourier series in each phase, so their exact gradients can be recovered from shifted photon-count measurements; Gaussian boson sampling under general loss admits no such finite rule.
Wideband two-port beam splitter of a binary fused- silica phase grating,
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Parameter-Shift Rules for Gradients in Boson Sampling Experiments
Lossy Fock boson sampling probabilities are finite Fourier series in each phase, so their exact gradients can be recovered from shifted photon-count measurements; Gaussian boson sampling under general loss admits no such finite rule.