A universal loss-limited optimum for fixed multi-pass quantum sensing per absorbed photon

How can we optimize quantum sensing schemes—such as phase estimation or object detection—when the sample being measured is fragile and prone to damage? The study seeks a universal figure of merit to determine the most efficient way to extract information per photon absorbed by the sample, rather than per photon sent.

The author analyzes multi-pass sensing schemes where a single photon is recycled through a sample multiple times. By defining a resource measure based on the number of photons actually absorbed by the object, the paper derives a general trade-off function, h(x) = x^2/(e^x - 1), where x represents the product of the number of passes and the loss per pass. This framework is applied to three distinct problems: interaction-free interrogation, phase estimation of weakly absorbing objects, and sub-Rayleigh detection of faint companions.

The study reveals that a single constant, x_opt = 1.594, dictates the optimal number of passes for a wide range of sensing tasks. The author proves that for fragile samples, the most efficient strategy is often the simplest: a single photon recycled through the sample. More complex strategies, such as using entangled N00N states, generally perform worse per absorbed photon because their fragility under loss outweighs their phase-sensitivity gains. Furthermore, for sub-Rayleigh discovery, the null-mode approach charges a fragile companion a fixed cost that is independent of its brightness, whereas direct imaging costs grow boundlessly as the companion becomes fainter.

This work provides a unified theoretical framework for quantum sensing, showing that seemingly disparate techniques are governed by the same underlying mathematical constraints. By identifying the universal optimum, researchers can better design experiments for sensitive biological or physical samples, ensuring maximum information gain while minimizing sample damage. It clarifies that for many practical applications, simple, low-loss, multi-pass setups are superior to more complex entangled-state strategies.