Semiclassical Geometric Tensor in Multiparameter Quantum Information

Year: 2026

Authors: Imai S., Yang J., Pezzè L.

Autors Affiliation: Univ Tsukuba, Inst Syst & Informat Engn, Tsukuba, Ibaraki 3058573, Japan; Univ Tsukuba, Ctr Artificial Intelligence Res C AIR, Tsukuba, Ibaraki 3058577, Japan; Consiglio Nazl Ric CNR INO, Ist Nazl Ott, Largo Enrico Fermi 6, I-50125 Florence, Italy; European Lab Nonlinear Spect LENS, Via N Carrara 1, I-50019 Sesto Fiorentino, Italy; Zhejiang Univ, Inst Quantum Sensing, Inst Fundamental & Transdisciplinary Res, Hangzhou 310027, Peoples R China; Zhejiang Univ, Inst Adv Study Phys, Hangzhou 310027, Peoples R China; KTH Royal Inst Technol, Nordita, Hannes Alfvens Vag 12, SE-10691 Stockholm, Sweden; Stockholm Univ, Hannes Alfvens Vag 12, SE-10691 Stockholm, Sweden.

Abstract: The discrepancy between quantum distinguishability in Hilbert space and classical distinguishability in probability space is expressed by the gap between the quantum and classical Fisher information matrices (QFIM and CFIM, respectively). This intrinsic quantum obstruction is generally not saturable and plays a central role in both fundamental insights and practical applications in modern quantum physics. Here, we develop a geometrical framework for this gap by introducing the notion of the semiclassical geometric tensor (SCGT). We relate this quantity to the quantum geometric tensor (QGT), whose real part equals the QFIM. We prove the matrix inequality between QGT and SCGT, which sharpens the standard inequality between QFIM and CFIM and provides novel multiparameter information bounds: the real part of the SCGT reproduces the CFIM plus an additional nonnegative contribution capturing quantum obstruction. This further motivates a natural extension of the Berry phase to the semiclassical setting.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 136 (15)      Pages from: 150801-1  to: 150801-9

More Information: We thank Francesco Albarelli, Leonardo Banchi, Hongzhen Chen, Balazs Heteny, Yutaka Shikano, Augusto Smerzi, Hiroyasu Tajima, Lingna Wang, Frank Wilczek, Benjamin Yadin, and Haidong Yuan for discussions. S. I. acknowledges support from Horizon Europe program HORIZON-CL4-2022-QUANTUM-02-SGA via the Project No. 101113690 (PASQuanS2.1) and JST ASPIRE (JPMJAP2339) . J. Y. acknowledges support from Zhejiang University start-up grants, Zhejiang Key Laboratory of R&D and Application of Cutting-Edge Scientific Instruments, and Wallenberg Initiative on Networks and Quantum Information (WINQ) . L. P. acknowledges support from the QuantERA project SQUEIS (Squeezing enhanced inertial sensing) , funded by the European Union ’ s Horizon Europe Program and the Agence Nationale de la Recherche (ANR-22-QUA2-0006) . This publication has received funding under the Horizon Europe program HORIZON-CL4-2022-QUANTUM-02-SGA via project 101113690 (PASQuanS2.1) .
KeyWords: Statistical Distance; Entanglement
DOI: 10.1103/3bwh-dhmv