SLD Fisher information for kinetic uncertainty relations

Abstract

We investigate a symmetric logarithmic derivative (SLD) Fisher information for kinetic uncertainty relations (KURs) of open quantum systems described by the GKSL quantum master equation with and without the detailed balance condition. In a quantum kinetic uncertainty relation derived by Vu and Saito [Phys. Rev. Lett. 128, 140602 (2022)], the Fisher information of probability of quantum trajectory with a time-rescaling parameter plays an essential role. This Fisher information is upper bounded by the SLD Fisher information. For a finite time and arbitrary initial state, we derive a concise expression of the SLD Fisher information, which is a double time integral and can be calculated by solving coupled first-order differential equations. We also derive a simple lower bound of the Fisher information of quantum trajectory. We point out that the SLD Fisher information also appears in the speed limit based on the Mandelstam-Tamm relation by Hasegawa [Nat. Commun. 14, 2828 (2023)]. When the jump operators connect eigenstates of the system Hamiltonian, we show that the Bures angle in the interaction picture is upper bounded by the square root of the dynamical activity at short times, which contrasts with the classical counterpart.

13 pages, 3 figures

References in corpus (20)

• Thermodynamic uncertainty relation for biomolecular processes
• Quantum trajectories and open many-body quantum systems
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects
• Violating the Thermodynamic Uncertainty Relation in the Three-Level Maser
• Thermodynamics of Precision in Markovian Open Quantum Dynamics
• Finite-Time Quantum Landauer Principle and Quantum Coherence
• Unified thermodynamic-kinetic uncertainty relation
• Unifying speed limit, thermodynamic uncertainty relation and Heisenberg principle via bulk-boundary correspondence
• Thermodynamic uncertainty relation for systems with unidirectional transitions
• Thermodynamics of precision in quantum nano-machines
• Thermodynamic uncertainty relations for coherently driven open quantum systems
• Thermodynamic uncertainty relation for first-passage times on Markov chains
• Housekeeping and excess entropy production for general nonlinear dynamics
• Kinetic uncertainty relation on first passage time for accumulated current
• Irreversibility, Loschmidt echo, and thermodynamic uncertainty relation
• Thermodynamic uncertainty relation for quantum first passage process
• Speed limits of the trace distance for open quantum system
• Thermodynamics of a continuous quantum heat engine: Interplay between population and coherence

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