Ultimate Precision of Direct Tomography of Wave Functions
In contrast to the standard quantum state tomography, the direct tomography seeks the direct access to the complex values of the wave function at particular positions (i.e., the expansion coefficient in a fixed basis). Originally put forward as a special case of weak measurement, it can be extended...
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ftdatacite:10.48550/arxiv.1911.07674 2023-05-15T18:32:42+02:00 Ultimate Precision of Direct Tomography of Wave Functions Nguyen, Xuan-Hoai Thi Choi, Mahn-Soo 2019 https://dx.doi.org/10.48550/arxiv.1911.07674 https://arxiv.org/abs/1911.07674 unknown arXiv https://dx.doi.org/10.1007/s11128-021-03167-0 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Quantum Physics quant-ph FOS Physical sciences article-journal Article ScholarlyArticle Text 2019 ftdatacite https://doi.org/10.48550/arxiv.1911.07674 https://doi.org/10.1007/s11128-021-03167-0 2022-03-10T16:20:07Z In contrast to the standard quantum state tomography, the direct tomography seeks the direct access to the complex values of the wave function at particular positions (i.e., the expansion coefficient in a fixed basis). Originally put forward as a special case of weak measurement, it can be extended to arbitrary measurement setup. We generalize the idea of "quantum metrology," where a real-valued phase is estimated, to the estimation of complex-valued phase, and apply it for the direct tomography of the wave function. It turns out that the reformulation can help us easily find the optimal measurements for efficient estimation. We further propose two different measurement schemes that eventually approach the Heisenberg limit. In the first scheme, the ensemble of measured system is duplicated and the replica ensemble is time-reversal transformed before the start of the measurement. In the other method, the pointers are prepared in special entangled states, either GHZ-like maximally entangled state or the symmetric Dicke state. In both methods, the real part of the parameter is estimated with a Ramsey-type interferometry while the imaginary part is estimated by amplitude measurements. : 15 pages; 1 figure Article in Journal/Newspaper The Pointers DataCite Metadata Store (German National Library of Science and Technology) |
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DataCite Metadata Store (German National Library of Science and Technology) |
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Quantum Physics quant-ph FOS Physical sciences |
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Quantum Physics quant-ph FOS Physical sciences Nguyen, Xuan-Hoai Thi Choi, Mahn-Soo Ultimate Precision of Direct Tomography of Wave Functions |
topic_facet |
Quantum Physics quant-ph FOS Physical sciences |
description |
In contrast to the standard quantum state tomography, the direct tomography seeks the direct access to the complex values of the wave function at particular positions (i.e., the expansion coefficient in a fixed basis). Originally put forward as a special case of weak measurement, it can be extended to arbitrary measurement setup. We generalize the idea of "quantum metrology," where a real-valued phase is estimated, to the estimation of complex-valued phase, and apply it for the direct tomography of the wave function. It turns out that the reformulation can help us easily find the optimal measurements for efficient estimation. We further propose two different measurement schemes that eventually approach the Heisenberg limit. In the first scheme, the ensemble of measured system is duplicated and the replica ensemble is time-reversal transformed before the start of the measurement. In the other method, the pointers are prepared in special entangled states, either GHZ-like maximally entangled state or the symmetric Dicke state. In both methods, the real part of the parameter is estimated with a Ramsey-type interferometry while the imaginary part is estimated by amplitude measurements. : 15 pages; 1 figure |
format |
Article in Journal/Newspaper |
author |
Nguyen, Xuan-Hoai Thi Choi, Mahn-Soo |
author_facet |
Nguyen, Xuan-Hoai Thi Choi, Mahn-Soo |
author_sort |
Nguyen, Xuan-Hoai Thi |
title |
Ultimate Precision of Direct Tomography of Wave Functions |
title_short |
Ultimate Precision of Direct Tomography of Wave Functions |
title_full |
Ultimate Precision of Direct Tomography of Wave Functions |
title_fullStr |
Ultimate Precision of Direct Tomography of Wave Functions |
title_full_unstemmed |
Ultimate Precision of Direct Tomography of Wave Functions |
title_sort |
ultimate precision of direct tomography of wave functions |
publisher |
arXiv |
publishDate |
2019 |
url |
https://dx.doi.org/10.48550/arxiv.1911.07674 https://arxiv.org/abs/1911.07674 |
genre |
The Pointers |
genre_facet |
The Pointers |
op_relation |
https://dx.doi.org/10.1007/s11128-021-03167-0 |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1911.07674 https://doi.org/10.1007/s11128-021-03167-0 |
_version_ |
1766216888274124800 |