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Title: Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements
Authors: Conlon, Lorcán O.
Suzuki, Jun
Lam, Ping Koy
Assad, Syed Muhamad
Keywords: Science::Physics
Issue Date: 2021
Source: 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-.
Journal: npj Quantum Information
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.
ISSN: 2056-6387
DOI: 10.1038/s41534-021-00414-1
Rights: © 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
Fulltext Permission: open
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