An arXiv preprint reports a conditional optimum for a class of fixed multi-pass quantum sensing schemes when performance is measured by the photons absorbed by the object. In the model, a single photon is sent through the object repeatedly, with m denoting the number of passes and L the loss on each pass. The analysis assumes that information grows quadratically with the number of passes, survival from one pass to the next is independent, and dose accumulates only along paths where the photon survives. Under those conditions, the trade-off is h(x) = x^2/(e^x - 1). It peaks at about 0.648 when the dimensionless pass-loss quantity x reaches 1.594.
The loss budget matters
The finding addresses a narrow but important question: does a universal loss-limited optimum exist when a photon can make several trips through a sample? The paper's answer is yes only for fixed arrangements that meet the stated assumptions. It presents the peak as a common ceiling for the analyzed fixed schemes, not as a blanket result for adaptive strategies.
The choice of resource is central. The paper counts photons absorbed by the object and excludes photons lost elsewhere. For weakly absorbing phase sensing, the best number of passes is set by total loss, including both parasitic and absorptive loss, while only the absorptive part is counted as damage to the sample.
In the paper's Zeno-interrogator example, the reported rate is capped at 0.2625/epsilon, with the optimum at 1.5936/epsilon cycles.
The paper draws a separate line around absorption estimation. It reports no super-linear scaling for that task, including entangled, adaptive and counterfactual strategies. That statement is distinct from the fixed-arrangement ceiling, which does not cover adaptive sensing.
How photon arrangements compare
Parallel entangled probes do not reach the same value under the paper's absorbed-photon convention. Their optimum is x = 1 with a value of 1/e, compared with x = 1.5936 and a value of 0.6476 for the sequential arrangement. The comparison is specifically about photons absorbed by the object.
When the analysis jointly varies pass number and photon number, it returns N = 1. The optimized value declines toward 0.368 as N grows. Within this modeled family, the result favors one recycled photon as the per-absorbed-photon choice.
An entangled Fock-family calculation gives a different but still bounded picture: its supremum is 0.868, approached but never attained, and the paper says it does not reach the single-photon benchmark.
A separate test for very close companions
In its analysis of symmetric, very small-separation cases, the paper reports that the advantage of null detection over direct imaging becomes unbounded as the separation tends to zero.
Under active illumination, the companion-normalized null rate is independent of the primary's properties. By contrast, the direct-imaging cost per certainty grows without bound as the companion becomes fainter. That advantage has a hard boundary in the model: below the crosstalk crossover, the absorbed-photon benefit of null detection disappears.
A ceiling with a narrow scope
The document is an arXiv v1 preprint dated 26 August 2026. It offers a rule for a defined family of fixed measurements, not a general answer for quantum sensing. The analysis excludes adaptive strategies, which the paper says can beat both fixed-arrangement ceilings. Its central result also depends on quadratic information growth, independent per-pass survival and dose accumulation along surviving paths.
Paper data and sources
Original title: A universal loss-limited optimum for fixed multi-pass quantum sensing per absorbed photon
Authors: Christoph F. Wildfeuer
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text