Asymmetric-Loss Equal-Born Test: a tabletop search for record-information-dependent optical loss

Standard linear optics requires that the transmittance of an optic be independent of photon number: for a linear element the input–output relation a_out = t·a_in + r·b_in is an operator identity, so single-photon and bright-light transmission are equal as a theorem rather than as an approximation. We are not aware of a dedicated test of that equality with a controlled scatterer at the 10⁻⁴ level. We state a hypothesis in which the equality fails in the single-quantum sector by a fixed dimensionless coupling λ*, and specify the tabletop experiment that would exclude it. The observable is Δ = D_quantum − D_classical, where D is the half-difference of a two-arm log-ratio under an ABBA swap of a weak scatterer, measured once with counting detectors and once with photodiodes through identical geometry. Standard quantum mechanics fixes Δ = 0 exactly; the hypothesis predicts Δ = −λ*·(−p ln p), or −0.046·λ* at a 1% transmission deficit. The loss map is stated as a photon-number-dependent Kraus channel, K = Σ exp[−½λ*·I_R(n)]|n⟩⟨n| with P_R(n) = 1 − (1−p)^n, which is linear, completely positive, local and non-signalling; invariance of a remote marginal is verified explicitly on a two-mode squeezed vacuum to 3×10⁻¹⁷. An earlier thermal formulation of the same idea is excluded by published SNSPD efficiency data at 2 K by a factor of 2×10⁵ and is withdrawn. An attempt to derive the criterion distinguishing which optical elements incur the cost failed under independent adversarial review and is reported as a failure; the surviving readings are converted into five pre-registered experimental arms with their nulls stated in advance. A borrowed teaching bench at 780 nm reaches a total uncertainty of 2.9×10⁻⁴ per operating point at 2×10⁸ counts, giving 5σ sensitivity at λ* ≥ 0.031 and 95% exclusion to 0.013 at a 1% scatterer; an extended scan through the turnover at p = 36.8% reaches 0.0039 and 0.0016 respectively, subject to a costed high-loss error-budget row and seven stated pass criteria. Five signatures distinguish the effect from systematics, including a −p ln p scaling and a maximum located at p = 0.368. The cheapest arm needs no interferometer: the single-photon versus bright transmission of one 50/50 beam splitter at 10⁻³, which bounds one reading of the hypothesis below λ* = 0.003 in an afternoon’s run on a prepared bench. The protocol is pre-registered before any bench is borrowed. The result will be published in either direction; a null is reported as the best bound in this sector.