Path Integral Approach to Quantum Fisher Information

• URL: http://arxiv.org/abs/2604.12763v1
• Date: Tue, 14 Apr 2026 14:06:20 GMT
• Title: Path Integral Approach to Quantum Fisher Information
• Abstract summary: We show that the quantum Fisher information can be expressed as a connected symmetrized covariance of a time-integrated action deformation.<n>This reformulation avoids explicit state reconstruction by rewriting the quantum Fisher information in terms of real-time correlators.
• Score: 1.0005747083373795
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\partial_λS$ 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.

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