Optimal local measurements in single-parameter quantum metrology

Anno: 2025

Autori: Liu JX., Yang J., Shi HL., Yu SX.

Affiliazione autori: Univ Sci & Technol China, Hefei Natl Res Ctr Phys Sci Microscale, Hefei 230026, Anhui, Peoples R China; Univ Sci & Technol China, Sch Phys Sci, Dept Modern Phys, Hefei 230026, Anhui, Peoples R China; KTH Royal Inst Technol, Nordita, Hannes Alfvens Vag 12, S-10691 Stockholm, Sweden; Stockholm Univ, Hannes Alfvens Vag 12, S-10691 Stockholm, Sweden; QSTAR, INO, CNR, Largo Enr Fermi 2, I-50125 Florence, Italy; LENS, Largo Enr Fermi 2, I-50125 Florence, Italy; Chinese Acad Sci, Innovat Acad Precis Measurement Sci & Technol, Wuhan 430071, Peoples R China; Univ Sci & Technol China, Hefei Natl Lab, Hefei 230088, Peoples R China.

Abstract: Quantum measurement plays a crucial role in quantum metrology. Due to the limitations of experimental capabilities, collectively measuring multiple copies of probing systems can present significant challenges. Therefore, the concept of locality in quantum measurements must be considered. In this work, we investigate the possibility of achieving the quantum Cram & eacute;r-Rao bound (QCRB) through local measurements (LMs). We first demonstrate that if there exists a LM to saturate the QCRB for qubit systems, then we can construct another rank-1 local projective measurement to saturate the QCRB. In this sense, rank-1 local projective measurements are sufficient to analyze the problem of saturating the QCRB. For pure qubits, we propose two necessary and sufficient methods to determine whether and how a given parameter estimation model can achieve the QCRB through LMs. The first method, dubbed the iterative matrix partition method and based on unitary transformations that render the diagonal entries of a traceless matrix vanish, elucidates the underlying mathematical structure of LMs as well as the local measurements with classical communications (LMCC), generalizing the result by Zhou et al. [Quantum Sci. Technol. 5, 025005 (2020)], which only holds for the later case. We clarify that the saturation of the QCRB through LMs for the Greenberger-Horne-Zeilinger-encoded states is actually due to the self-similar structure in this approach. The second method, dubbed the hierarchy of orthogonality conditions and based on the parametrization of rank-1 measurements for qubit systems, allows us to construct several examples of saturating QCRBs, including the three-qubit W states and the N-qubit W states (N 3). Our findings offer insights into achieving optimal performance in quantum metrology when measurement resources are limited.

Giornale/Rivista: PHYSICAL REVIEW A

Volume: 111 (2)      Da Pagina: 22436-1  A: 22436-9

Maggiori informazioni: We thank Sisi Zhou for useful comments on the manuscript. J.Y. was funded by the Wallenberg Initiative on Networks and Quantum Information (WINQ) . H.L.S. was supported by the European Commission through the H2020 QuantERA ERA-NET Cofund in Quantum Technologies project MENTA and the NSFC under Key Grants No. 12134015 and No. 92365202. S.X.Y. was supported by the Key-Area Research and Development Program of Guangdong Province under Grant No. 2020B0303010001.
Parole chiavi: Local measurement; Local projective; Probing system; Projective measurement; Quantum Cramer-Rao bounds; Quantum measurement; Quantum metrology; Qubit system; Single parameter; W state
DOI: 10.1103/PhysRevA.111.022436