Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements
Abstract 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 Cr...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2021-07-01
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| Series: | npj Quantum Information |
| Online Access: | https://doi.org/10.1038/s41534-021-00414-1 |
| _version_ | 1828971263228379136 |
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| author | Lorcán O. Conlon Jun Suzuki Ping Koy Lam Syed M. Assad |
| author_facet | Lorcán O. Conlon Jun Suzuki Ping Koy Lam Syed M. Assad |
| author_sort | Lorcán O. Conlon |
| collection | DOAJ |
| description | Abstract 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 | 2024-12-14T13:06:59Z |
| format | Article |
| id | doaj.art-84a0a1f8124140e9b9efac5dc6e6f07b |
| institution | Directory Open Access Journal |
| issn | 2056-6387 |
| language | English |
| last_indexed | 2024-12-14T13:06:59Z |
| publishDate | 2021-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Quantum Information |
| spelling | doaj.art-84a0a1f8124140e9b9efac5dc6e6f07b2022-12-21T23:00:18ZengNature Portfolionpj Quantum Information2056-63872021-07-01711810.1038/s41534-021-00414-1Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurementsLorcán O. Conlon0Jun Suzuki1Ping Koy Lam2Syed M. Assad3Department of Quantum Science, Centre for Quantum Computation and Communication Technology, Australian National UniversityGraduate School of Informatics and Engineering, The University of Electro-CommunicationsDepartment of Quantum Science, Centre for Quantum Computation and Communication Technology, Australian National UniversityDepartment of Quantum Science, Centre for Quantum Computation and Communication Technology, Australian National UniversityAbstract 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.https://doi.org/10.1038/s41534-021-00414-1 |
| spellingShingle | Lorcán O. Conlon Jun Suzuki Ping Koy Lam Syed M. Assad Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements npj Quantum Information |
| 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 |
| url | https://doi.org/10.1038/s41534-021-00414-1 |
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