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Path integral approach to the quantum fidelity amplitude
1Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland jiri.vanicek@epfl.ch.
Summary
The Loschmidt echo measures quantum irreversibility using fidelity amplitude. New path integral methods provide accurate semiclassical approximations for fidelity amplitude, improving quantum mechanics understanding and applications.
Area of Science:
- Quantum Mechanics
- Quantum Information Theory
Background:
- The Loschmidt echo quantifies quantum irreversibility.
- Fidelity amplitude is crucial for quantum mechanics foundations and applications like spectroscopy.
Purpose of the Study:
- Derive an exact path integral formula for fidelity amplitude.
- Develop accurate semiclassical approximations for fidelity amplitude.
Main Methods:
- Path integral formulation.
- Truncation of path integral expansion for semiclassical approximations.
- Analysis of zeroth, first, and second-order expansions.
Main Results:
- An exact path integral formula for fidelity amplitude was derived.
- Zeroth-order expansion provides a simple, non-trivial approximation.
- First-order expansion offers an alternative derivation of the dephasing representation.
- Second-order expansion yields an improved fidelity approximation.
Conclusions:
- The path integral approach rigorously derives fidelity amplitude approximations.
- Identified conditions for the exactness of various approximations.
- The study enhances understanding of quantum irreversibility and time-reversal protocols.
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