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Generalized geometric speed limits for quantum observables

Jacob Bringewatt1,2,3,4,*, Zach Steffen5,6, Martin A. Ritter3, Adam Ehrenberg2,3, Haozhi Wang5,6, B. S. Palmer5,6, Alicia J. Kollár3, Alexey V. Gorshkov2,3, and Luis Pedro García-Pintos7

  • *Contact author: bringewa@usna.edu
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Phys. Rev. Research 7, 033222 – Published 4 September, 2025

DOI: https://doi.org/10.1103/h6lj-d6yt

Abstract

Leveraging quantum information geometry, we derive generalized quantum speed limits on the rate of change of the expectation values of observables. These bounds subsume and, for Hilbert space dimension ≥3, tighten existing bounds—in some cases by an arbitrarily large multiplicative constant. Our theoretical results are supported by illustrative examples and an experimental demonstration using a superconducting qutrit. We also derive two upper bounds on the generalized quantum Fisher information in terms of the condition number of the density matrix. One of these bounds applies only to coherent dynamics and depends also on the variance of the Hamiltonian. The other bound depends also on the so-called Wigner-Yanase skew information. These bounds generalize well-known bounds on the symmetric logarithmic derivative quantum Fisher information and are tighter than the existing bounds for sufficiently mixed states (e.g., for sufficiently high temperature thermal states).

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Outline

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Phys. Rev. Research 7, 033222– Published 4 September, 2025
  • Received 16 September 2024
  • Revised 3 June 2025
  • Accepted 20 August 2025
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