Small entangled quantum states combined with repeated passes through an interferometer outperformed the standard NOON-state approach in a theoretical comparison under loss, according to a new arXiv preprint. The advantage appeared when the resource was counted as particle-passes—the measure used in the analysis for repeated interactions with the phase being estimated.
The result is a calculation, not an experimental demonstration. The paper compares mathematical models of different two-mode photon states inside a lossy multipass Mach–Zehnder interferometer, a device in which light travels through the sensing arrangement repeatedly. Its conclusions therefore apply to the specified model, settings and measurement scheme rather than establishing how a working instrument would perform.
Why repeated passes help — and then hurt
The basic tension is straightforward: additional passes allow the state to accumulate more phase information, but they also expose it to more opportunities for loss. In the paper’s test of ordinary NOON states, that trade-off produced a clear peak. For states containing one, two or five particles, the quantum Fisher information per particle-pass first increased with the number of passes and then declined at a per-pass transmission of η = 0.95.
Quantum Fisher information, or QFI, is the paper’s theoretical benchmark for the information a probe state can carry about the unknown phase. The analysis uses the quantum Cramér–Rao bound in an asymptotic setting, meaning it describes the limit reached with many independent measurements. All three displayed NOON-state sizes reached the same maximum QFI per particle-pass in that comparison, even though their performance fell after too many passes.
Four photons, but more than one way to entangle them
The main state comparison focused on N = 4, or four photons. It examined standard NOON states alongside flat states, BAT states and rotated NOON states. The authors describe the four-photon BAT and NOON states included in the comparison as having already been experimentally realized, but the comparison itself is theoretical rather than an experimental demonstration.
At η = 0.95, both the flat and BAT states reached a higher maximum QFI per particle-pass than the standard NOON state. The rotated NOON state performed better than both NOON and BAT, and it marginally exceeded the flat state in the QFI comparison. The model therefore favored the rotated NOON option over the standard NOON benchmark and, by a small margin, the flat state.
For the stated four-photon setting and η = 0.95, the best rotated NOON configuration used 17 passes and a beam-splitter reflectivity of 0.83. Those values are modeled optima for the parameter scan reported in the paper; no uncertainty around the optimum was given.
A simpler measurement keeps the ranking
The study also tested a more concrete read-out rather than relying only on the QFI benchmark. The modeled measurement sends the output through a beam splitter and counts the number of particles emerging from each output, while optimizing the operating phase and relevant beam-splitter reflectivities. This produces a classical Fisher information value: the information available from that specified counting procedure.
At η = 0.95, the plotted classical Fisher information per particle-pass for BAT and rotated NOON states was higher than for the simple NOON case. Across every per-pass transmission value shown in the paper, the ordering remained the same: rotated NOON first, BAT second and NOON third. The rotated NOON state therefore led both the paper’s QFI comparison and its selected photon-counting comparison.
A proposal still waiting for a laboratory test
The authors present the approach as a possible practical route to quantum-enhanced metrology in lossy environments, especially when particle-passes are the constrained resource. But they describe the work as a proof-of-principle implementation and say that an experiment would require control over the number of passes. No such experimental demonstration is reported in the supplied work.
The model also sets clear boundaries around the claim. It treats loss as occurring through imperfect cavity-mirror reflection in the sensing arm while the reference arm is effectively lossless. The main state comparison is limited to small four-photon states, and the practical comparison uses one specified counting measurement. The calculations use asymptotic estimation theory, so they do not answer how the proposal would perform with finite data.
The work is identified as an arXiv preprint, version 1, dated 26 Aug 2026. The authors report funding from the United Kingdom EPSRC through the Quantum Information Science and Technology Centre for Doctoral Training. An experimental test would require control of the number of passes.
Paper data and sources
Original title: Enhanced quantum metrology with robust multipass interferometry
Authors: Sayak Mukherjee, José Afonso Oliveira, Sean William Moore, Jacob A. Dunningham
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text