Quantum speed limit for Kirkwood-Dirac quasiprobabilities

Year: 2025

Authors: Pratapsi S.S., Deffner S., Gherardini S.

Autors Affiliation: Univ Coimbra, Dept Phys, CFisUC, P-3004516 Coimbra, Portugal; Univ Lisbon, Inst Super Tecn, P-1049001 Lisbon, Portugal; Inst Telecomunicacoes, P-1049001 Lisbon, Portugal; Univ Maryland, Dept Phys, Baltimore, MD 21250 USA; Univ Maryland, Quantum Sci Inst, Baltimore, MD 21250 USA; Natl Quantum Lab, College Pk, MD 20740 USA; Consiglio Nazl Ric CNR INO, Ist Nazl Ott, Largo Enr Fermi 6, I-50125 Florence, Italy; Univ Firenze, European Lab Nonlinear Spect, I-50019 Sesto Fiorentino, Italy.

Abstract: What is the minimal time until a quantum system undergoing unitary dynamics can exhibit genuine quantum features’ To answer this question we derive quantum speed limits (QSLs) for two-time correlation functions arising from statistics of measurements. These two-time correlators are described by Kirkwood-Dirac quasiprobabilities, if the initial quantum state of the system does not commute with the measurement observables. The QSLs here introduced are derived from the Schr & ouml;dinger-Robertson uncertainty relation, and set the minimal time at which the real part of a quasiprobability can become negative and the corresponding imaginary part can be different from zero or crosses a given threshold. This departure of Kirkwood-Dirac quasiprobabilities from positivity is evidence for the onset of non-classical traits in the quantum dynamics. As an illustrative example, we apply these results to a conditional quantum gate by determining the optimal condition that gives rise to non-classicality at maximum speed. In this way, our analysis hints at boosted power extraction due to genuinely non-classical dynamics.

Journal/Review: QUANTUM SCIENCE AND TECHNOLOGY

Volume: 10 (3)      Pages from: 35019-1  to: 35019-14

More Information: S S P acknowledges support from the ’la Caixa’ foundation through scholarship No. LCF/BQ/DR20/11790030, and from national funds by FCT-Fundacao para a Ciencia e Tecnologia, I.P., through scholarship 2023.01162.BD, and in the framework of the Projects UIDB/04564/2020 and UIDP/04564/2020, with DOI identifiers https://doi.org/10.54499/UIDB/04564/2020 and https://doi.org/10.54499/UIDP/04564/2020, respectively. S G acknowledges financial support from the Project PRIN 2022 Quantum Reservoir Computing (QuReCo), the PNRR MUR Project PE0000023-NQSTI financed by the European Union-Next Generation EU, and the MISTI Global Seed Funds MIT-FVG Collaboration Grant ’Revealing and exploiting quantumness via quasiprobabilities: from quantum thermodynamics to quantum sensing’. S D acknowledges support from the U.S. National Science Foundation under Grant No. DMR-2010127 and the John Templeton Foundation under Grant No. 62422.
KeyWords: quantum; Kirkwood-Dirac; quasiprobabilities; quantum speed limit
DOI: 10.1088/2058-9565/add55d