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  • Open Access

Semiclassical Geometric Tensor in Multiparameter Quantum Information

Satoya Imai1,2,3,4,*, Jing Yang5,6,†, and Luca Pezzè3,4,‡

  • *Contact author: satoyaimai@yahoo.co.jp
  • †Contact author: jing.yang.quantum@zju.edu.cn
  • ‡Contact author: luca.pezze@ino.cnr.it
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Phys. Rev. Lett. 136, 150801 – Published 17 April, 2026

DOI: https://doi.org/10.1103/3bwh-dhmv

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.

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Phys. Rev. Lett. 136, 150801– Published 17 April, 2026
  • Received 21 May 2025
  • Revised 30 November 2025
  • Accepted 24 March 2026
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