Symmetric-logarithmic-derivative Fisher information for kinetic uncertainty relations
Satoshi Nakajima1, Yasuhiro Utsumi1
1Department of Physics Engineering, Faculty of Engineering, Mie University, Tsu, Mie 514-8507, Japan.
Physical Review. E
|December 20, 2023
Summary
We derived a new expression for symmetric logarithmic derivative (SLD) Fisher information in open quantum systems, crucial for quantum kinetic uncertainty relations (KURs) and quantum speed limits.
Area of Science:
- Quantum Information Theory
- Open Quantum Systems
Background:
- Kinetic uncertainty relations (KURs) are vital for understanding quantum system dynamics.
- The Fisher information of quantum trajectories plays a key role in KURs.
Purpose of the Study:
- To investigate symmetric logarithmic derivative (SLD) Fisher information for KURs in open quantum systems.
- To derive a concise expression and bounds for SLD Fisher information.
Main Methods:
- Utilizing the GKSL quantum master equation with and without detailed balance.
- Deriving a double time integral expression for SLD Fisher information.
- Solving coupled first-order differential equations.
Main Results:
- A concise expression for SLD Fisher information for finite time and arbitrary initial states was derived.
- A simple lower bound for quantum trajectory Fisher information was established.
- The connection between SLD Fisher information and Mandelstam-Tamm based speed limits was highlighted.
Conclusions:
- The derived SLD Fisher information expression offers a computable method for analyzing quantum dynamics.
- The study provides new insights into the bounds and applications of Fisher information in open quantum systems.
- A contrast with classical systems was observed regarding Bures angle and dynamical activity.
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