Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements
Finding the optimal attainable precisions in quantum multiparameter metrology is a non-trivial problem. One approach to tackling this problem involves the computation of bounds which impose limits on how accurately we can estimate certain physical quantities. One such bound is the Holevo Cramér–Rao...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Language: | English |
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2021
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| Online Access: | https://hdl.handle.net/10356/153821 |
| _version_ | 1824456164647108608 |
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| author | Conlon, Lorcán O. Suzuki, Jun Lam, Ping Koy Assad, Syed Muhamad |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Conlon, Lorcán O. Suzuki, Jun Lam, Ping Koy Assad, Syed Muhamad |
| author_sort | Conlon, Lorcán O. |
| collection | NTU |
| description | Finding the optimal attainable precisions in quantum multiparameter metrology is a non-trivial problem. One approach to tackling this problem involves the computation of bounds which impose limits on how accurately we can estimate certain physical quantities. One such bound is the Holevo Cramér–Rao bound on the trace of the mean squared error matrix. The Holevo bound is an asymptotically achievable bound when one allows for any measurement strategy, including collective measurements on many copies of the probe. In this work, we introduce a tighter bound for estimating multiple parameters simultaneously when performing separable measurements on a finite number of copies of the probe. This makes it more relevant in terms of experimental accessibility. We show that this bound can be efficiently computed by casting it as a semidefinite programme. We illustrate our bound with several examples of collective measurements on finite copies of the probe. These results have implications for the necessary requirements to saturate the Holevo bound. |
| first_indexed | 2025-02-19T03:49:45Z |
| format | Journal Article |
| id | ntu-10356/153821 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:49:45Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1538212023-02-28T20:00:27Z Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements Conlon, Lorcán O. Suzuki, Jun Lam, Ping Koy Assad, Syed Muhamad School of Physical and Mathematical Sciences Science::Physics Quantum Information Quantum Metrology Finding the optimal attainable precisions in quantum multiparameter metrology is a non-trivial problem. One approach to tackling this problem involves the computation of bounds which impose limits on how accurately we can estimate certain physical quantities. One such bound is the Holevo Cramér–Rao bound on the trace of the mean squared error matrix. The Holevo bound is an asymptotically achievable bound when one allows for any measurement strategy, including collective measurements on many copies of the probe. In this work, we introduce a tighter bound for estimating multiple parameters simultaneously when performing separable measurements on a finite number of copies of the probe. This makes it more relevant in terms of experimental accessibility. We show that this bound can be efficiently computed by casting it as a semidefinite programme. We illustrate our bound with several examples of collective measurements on finite copies of the probe. These results have implications for the necessary requirements to saturate the Holevo bound. Published version This work was supported by the Australian Research Council (ARC) under the Centre of Excellence for Quantum Computation and Communication Technology (Grant No. CE170100012). J.S. was supported by the UEC Research Support Program, the University of Electro-Communications. The authors are grateful to Professor Nagaoka and Professor Hayashi for helpful discussions. 2021-12-30T00:39:27Z 2021-12-30T00:39:27Z 2021 Journal Article Conlon, L. O., Suzuki, J., Lam, P. K. & Assad, S. M. (2021). Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements. Npj Quantum Information, 7(1), 110-. https://dx.doi.org/10.1038/s41534-021-00414-1 2056-6387 https://hdl.handle.net/10356/153821 10.1038/s41534-021-00414-1 2-s2.0-85110634359 1 7 110 en npj Quantum Information © 2021 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. application/pdf |
| spellingShingle | Science::Physics Quantum Information Quantum Metrology Conlon, Lorcán O. Suzuki, Jun Lam, Ping Koy Assad, Syed Muhamad Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements |
| title | Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements |
| title_full | Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements |
| title_fullStr | Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements |
| title_full_unstemmed | Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements |
| title_short | Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements |
| title_sort | efficient computation of the nagaoka hayashi bound for multiparameter estimation with separable measurements |
| topic | Science::Physics Quantum Information Quantum Metrology |
| url | https://hdl.handle.net/10356/153821 |
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