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Quantum Simulation

KAM-Stability for Conserved Quantities in Finite-Dimensional Quantum Systems

arXiv
Authors: Daniel Burgarth, Paolo Facchi, Hiromichi Nakazato, Saverio Pascazio, Kazuya Yuasa

Year

2020

Paper ID

19436

Status

Preprint

Abstract Read

~2 min

Abstract Words

84

Citations

N/A

Abstract

We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries small perturbations can lead to large deviations over long times, while for robust symmetries their expectation values remain close to their initial values for all times. This is in analogy with the celebrated Kolmogorov-Arnold-Moser (KAM) theorem in classical mechanics. To prove this remarkable result, we introduce a resummation of a perturbation series, which generalizes the Hamiltonian of the quantum Zeno dynamics.

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  • We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries small...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2011.04707 [2] arXiv https://arxiv.org/abs/2011.04707 [3] Publisher https://arxiv.org/abs/2011.04707

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