Path Integral Approach to Quantum Fisher Information
Abstract
We present a real-time path-integral formulation of the quantum Fisher information for dynamical parameter estimation. For pure states undergoing unitary evolution, we show that the quantum Fisher information can be expressed as a connected symmetrized covariance of a time-integrated action deformation, equivalently as an integrated insertion of in the propagator. This reformulation avoids explicit state reconstruction by rewriting the quantum Fisher information in terms of real-time correlators that are natural targets for many-body methods. We further embed the construction into the Schwinger-Keldysh closed-time-path formalism, identifying the quantum Fisher information with the Keldysh component of an appropriate contour-ordered correlator generated by forward and backward propagating sources. Finally, using the Van Vleck-Gutzwiller approximation we re-derive the compact semiclassical quantum Fisher information expression, clarifying how classical trajectory data control leading-order metrological sensitivity.
Cite
@article{arxiv.2604.12763,
title = {Path Integral Approach to Quantum Fisher Information},
author = {Francis J. Headley and Mahdi RouhbakhshNabati and Henry Harper-Gardner and Daniel Braun and Henning Schomerus and Emre Köse},
journal= {arXiv preprint arXiv:2604.12763},
year = {2026}
}