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Information geometry aspects of minimum entropy production paths from quantum mechanical evolutions
1SUNY Polytechnic Institute, Albany, New York 12203, USA.
Physical Review. E
|March 15, 2020
Summary
We analyze quantum state transfers using information geometry, finding that faster transfers correlate with higher entropy production rates. This reveals a trade-off between speed and efficiency in quantum systems.
Area of Science:
- Quantum Information Theory
- Statistical Mechanics
- Geometric Mechanics
Background:
- Quantum search schemes utilize time-dependent Hamiltonians to evolve quantum states.
- Information geometry provides tools to analyze the geometry of quantum state spaces.
- Entropy production is a key concept in understanding irreversible processes.
Purpose of the Study:
- To investigate the relationship between entropic speeds and entropy production rates during quantum state transfer.
- To analyze geodesic evolution on manifolds of parametrized quantum states.
- To explore the efficiency of analog quantum search schemes.
Main Methods:
- Information geometric analysis of entropic speeds and entropy production rates.
- Utilizing Fisher information for Riemannian metrization on quantum state manifolds.
- Employing a minimum action method for quantum state transfer.
Main Results:
- The optimal quantum state transfer path is a geodesic, minimizing both transfer time and total entropy production.
- A direct quantitative relationship is established: faster quantum transfers result in higher entropy production rates.
- Lower entropic efficiency is shown to accompany higher entropic speeds in quantum transfer processes.
Conclusions:
- The study quantifies the trade-off between speed and entropy production in quantum state transfers.
- Findings have implications for optimizing analog quantum search schemes and understanding quantum thermodynamics.
- Geodesic paths represent the most efficient, albeit entropy-producing, routes for quantum state manipulation.
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