dorsal/arxiv
View SchemaHadamard Products of Product Operators and the Design of Gradient-Diffusion Experiments for Simulating Decoherence by NMR Spectroscopy
| Authors | Timothy F. Havel, Yehuda Sharf, Lorenza Viola, David G. Cory |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0009010 |
| URL | https://arxiv.org/abs/quant-ph/0009010 |
| DOI | 10.1016/S0375-9601(01)00083-4 |
| Journal | Physics Letters A, vol. 280, nos. 5-6, pp. 282-288 (2001) |
Abstract
An extension of the product operator formalism of NMR is introduced, which uses the Hadamard matrix product to describe many simple spin 1/2 relaxation processes. The utility of this formalism is illustrated by deriving NMR gradient-diffusion experiments to simulate several decoherence models of interest in quantum information processing, along with their Lindblad and Kraus representations. Gradient-diffusion experiments are also described for several more complex forms of decoherence, including the well-known collective isotropic model. Finally, it is shown that the Hadamard formalism gives a concise representation of decoherence with arbitrary correlations among the fluctuating fields at the different spins involved, and that this can be applied to both decoherence (T2) as well as nonadiabatic relaxation (T1) processes.
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"abstract": "An extension of the product operator formalism of NMR is introduced, which\nuses the Hadamard matrix product to describe many simple spin 1/2 relaxation\nprocesses. The utility of this formalism is illustrated by deriving NMR\ngradient-diffusion experiments to simulate several decoherence models of\ninterest in quantum information processing, along with their Lindblad and Kraus\nrepresentations. Gradient-diffusion experiments are also described for several\nmore complex forms of decoherence, including the well-known collective\nisotropic model. Finally, it is shown that the Hadamard formalism gives a\nconcise representation of decoherence with arbitrary correlations among the\nfluctuating fields at the different spins involved, and that this can be\napplied to both decoherence (T2) as well as nonadiabatic relaxation (T1)\nprocesses.",
"arxiv_id": "quant-ph/0009010",
"authors": [
"Timothy F. Havel",
"Yehuda Sharf",
"Lorenza Viola",
"David G. Cory"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/S0375-9601(01)00083-4",
"journal_ref": "Physics Letters A, vol. 280, nos. 5-6, pp. 282-288 (2001)",
"title": "Hadamard Products of Product Operators and the Design of Gradient-Diffusion Experiments for Simulating Decoherence by NMR Spectroscopy",
"url": "https://arxiv.org/abs/quant-ph/0009010"
},
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