Quantum estimation with state symmetry-induced optimal measurements
Year: 2026
Authors: Liu JX., Shi HL., Wu CF., Yu SX.
Autors Affiliation: Univ Sci & Technol China, Hefei Natl Res Ctr Phys Sci Microscale, Dept Modern Phys, Hefei, Anhui, Peoples R China; Univ Sci & Technol China, Sch Phys Sci, Dept Modern Phys, Hefei, Anhui, Peoples R China; CNR, INO, Florence, Italy; LENS, Florence, Italy; Singapore Univ Technol & Design, Sci Math & Technol, Singapore, Singapore; Univ Sci & Technol China, Hefei Natl Lab, Hefei, Peoples R China.
Abstract: A central challenge in quantum metrology is identifying optimal measurements that saturate the quantum Cram & eacute;r-Rao bound under realistic constraints, e.g., local measurements. We show that symmetries of the probe state provide a general principle for identifying optimal measurement strategies. Building on this idea, we demonstrate that when a parameter is encoded in the real coefficients of a fixed-basis expansion, the optimal measurement reduces to projection in that basis, with an application to critical metrology. Under local-measurement constraints, we show that local state symmetries provide a systematic route to constructing optimal local measurements. We illustrate this framework using graph states, explicitly constructing optimal local measurements from their local symmetries. Furthermore, weak and strong connection rules are introduced to generate broader classes of graph states that achieve Heisenberg-scaling precision using local measurements. By relaxing the number of stabilizer generators, graph states are extended to a stabilizer-code subspace. Analytical and numerical results show that coherent states in these subspaces offer multiple metrological advantages: high precision, partial noise resilience, local-measurement accessibility, and built-in error correction. These findings advance the theory of optimal measurements in quantum metrology and underscore the central role of state symmetry.
Journal/Review: NATURE COMMUNICATIONS
Volume: 17 (1) Pages from: 7898-1 to: 7898-13
More Information: J.-X. Liu declares no relevant funding for this work. H.-L. Shi discloses support for the research of this work from the European Commission [H2020 QuantERA ERA-NET Cofund, project MENTA] and Horizon Europe [HORIZONCL4-2022-QUANTUM-02-SGA, project 101113690 (PASQuanS2.1)]. C. Wu discloses support for the research of this work from the National Research Foundation, Singapore and A*STAR under its Quantum Engineering Programme [NRF2021-QEP2-02-P03]. S. Yu discloses support for publication of this work from Quantum Science and Technology-National Science and Technology Major Project [2021ZD0300804].KeyWords: InformationDOI: 10.1038/s41467-026-73507-0
