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Generalized geometric speed limits for quantum observables

Bringewatt, Jacob [US Naval Academy, Annapolis, MD (United States); Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States); Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute; Harvard Univ., Cambridge, MA (United States)] (ORCID:0000000332353444)·Steffen, Zach [Univ. of Maryland, College Park, MD (United States). Maryland Quantum Materials Center; Laboratory for Physical Sciences, College Park, MD (United States)] (ORCID:0000000209710901)·Ritter, Martin A. [Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute] (ORCID:0000000342350781)·Ehrenberg, Adam [Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States); Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute] (ORCID:0000000231676519)·Wang, Haozhi [Univ. of Maryland, College Park, MD (United States). Maryland Quantum Materials Center; Laboratory for Physical Sciences, College Park, MD (United States)] (ORCID:000000029788357X)·Palmer, B. S. [Univ. of Maryland, College Park, MD (United States). Maryland Quantum Materials Center; Laboratory for Physical Sciences, College Park, MD (United States)] (ORCID:000000021259995X)·Kollár, Alicia J. [Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute] (ORCID:0009000320194594)·Gorshkov, Alexey V. [Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States); Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute] (ORCID:0000000305093421)·García-Pintos, Luis Pedro [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000320754996)
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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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Bringewatt, Jacob [US Naval Academy, Annapolis, MD (United States); Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States); Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute; Harvard Univ., Cambridge, MA (United States)] (ORCID:0000000332353444), Steffen, Zach [Univ. of Maryland, College Park, MD (United States). Maryland Quantum Materials Center; Laboratory for Physical Sciences, College Park, MD (United States)] (ORCID:0000000209710901), Ritter, Martin A. [Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute] (ORCID:0000000342350781), Ehrenberg, Adam [Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States); Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute] (ORCID:0000000231676519), Wang, Haozhi [Univ. of Maryland, College Park, MD (United States). Maryland Quantum Materials Center; Laboratory for Physical Sciences, College Park, MD (United States)] (ORCID:000000029788357X), Palmer, B. S. [Univ. of Maryland, College Park, MD (United States). Maryland Quantum Materials Center; Laboratory for Physical Sciences, College Park, MD (United States)] (ORCID:000000021259995X), Kollár, Alicia J. [Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute] (ORCID:0009000320194594), Gorshkov, Alexey V. [Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States); Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute] (ORCID:0000000305093421), García-Pintos, Luis Pedro [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000320754996). 2025-09-04. Generalized geometric speed limits for quantum observables. https://doi.org/10.1103/h6lj-d6yt

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