Abstract

Point tomography is an approach to the problem of state estimation, which is arguably the most efficient and simple method for modern high-precision quantum information experiments. In this scenario, the experimenter knows the target state that their device should prepare, except that intrinsic systematic errors will create small discrepancies in the state actually produced. By introducing a kind of informationally complete measurement, dubbed Fisher-symmetric measurements, point tomography determines deviations from the expected state with optimal efficiency. Moreover, the number of outcomes of a measurement saturating the Gill-Massar limit for reconstructing d-dimensional quantum states can be greatly reduced from ?4d-3 to only 2d-1 outcomes. Thus, improving the measurement overhead as the dimension increases. Here we demonstrate the experimental viability of point tomography. Using a modern photonic platform constructed with state-of-the-art multicore optical fiber technology, we generate four-dimensional quantum states and implement seven-outcome Fisher-symmetric measurements. Our experimental results exhibit the main feature of point tomography, namely, a precision close to the Gill-Massar limit with a single few-outcome measurement. Specifically, we achieved a precision of (3.81±0.05)/N, while the Gill-Massar limit for d=4 is 3/N (N being the ensemble size). © 2025 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.