dorsal/arxiv
View SchemaFidelity Decay as an Efficient Indicator of Quantum Chaos
| Authors | Joseph Emerson, Yaakov S. Weinstein, Seth Lloyd, D. G. Cory |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0207099 |
| URL | https://arxiv.org/abs/quant-ph/0207099 |
| DOI | 10.1103/PhysRevLett.89.284102 |
| Journal | Phys. Rev. Lett. 89, 284102 (2002) |
Abstract
Recent work has connected the type of fidelity decay in perturbed quantum models to the presence of chaos in the associated classical models. We demonstrate that a system's rate of fidelity decay under repeated perturbations may be measured efficiently on a quantum information processor, and analyze the conditions under which this indicator is a reliable probe of quantum chaos and related statistical properties of the unperturbed system. The type and rate of the decay are not dependent on the eigenvalue statistics of the unperturbed system, but depend on the system's eigenvector statistics in the eigenbasis of the perturbation operator. For random eigenvector statistics the decay is exponential with a rate fixed precisely by the variance of the perturbation's energy spectrum. Hence, even classically regular models can exhibit an exponential fidelity decay under generic quantum perturbations. These results clarify which perturbations can distinguish classically regular and chaotic quantum systems.
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"abstract": "Recent work has connected the type of fidelity decay in perturbed quantum\nmodels to the presence of chaos in the associated classical models. We\ndemonstrate that a system\u0027s rate of fidelity decay under repeated perturbations\nmay be measured efficiently on a quantum information processor, and analyze the\nconditions under which this indicator is a reliable probe of quantum chaos and\nrelated statistical properties of the unperturbed system. The type and rate of\nthe decay are not dependent on the eigenvalue statistics of the unperturbed\nsystem, but depend on the system\u0027s eigenvector statistics in the eigenbasis of\nthe perturbation operator. For random eigenvector statistics the decay is\nexponential with a rate fixed precisely by the variance of the perturbation\u0027s\nenergy spectrum. Hence, even classically regular models can exhibit an\nexponential fidelity decay under generic quantum perturbations. These results\nclarify which perturbations can distinguish classically regular and chaotic\nquantum systems.",
"arxiv_id": "quant-ph/0207099",
"authors": [
"Joseph Emerson",
"Yaakov S. Weinstein",
"Seth Lloyd",
"D. G. Cory"
],
"categories": [
"quant-ph",
"nlin.CD"
],
"doi": "10.1103/PhysRevLett.89.284102",
"journal_ref": "Phys. Rev. Lett. 89, 284102 (2002)",
"title": "Fidelity Decay as an Efficient Indicator of Quantum Chaos",
"url": "https://arxiv.org/abs/quant-ph/0207099"
},
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