Uncertainty relations between quantum Fisher information and entanglement monotones
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912976807657472 |
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| author | Du, Shaowei Liu, Shuheng Fadel, Matteo Vitagliano, Giuseppe He, Qiongyi |
| author_facet | Du, Shaowei Liu, Shuheng Fadel, Matteo Vitagliano, Giuseppe He, Qiongyi |
| contents | Entanglement is widely regarded as an essential resource for a number of tasks and can in some cases be quantified by figures of merit related to those tasks. In quantum metrology, this is showcased by the connections between the quantum Fisher information (QFI), providing a bound to the precision, and multipartite entanglement quantifiers such as the entanglement depth. However, a connection between the QFI and entanglement monotones, i.e., functions that do not increase under Local Operations and Classical Communications, has so far remained elusive. In this work, we fill this gap by introducing a family of uncertainty relations that bound bipartite entanglement monotones from below via elements of a quantum Fisher information matrix. To further emphasize the significance of our results, we connect these relations to the achievable precision in multiparameter estimation. Considering a system split into two parts with arbitrary dimension, we also show that, while two-dimensional entanglement is sufficient to estimate a single parameter with maximal precision, genuine high-dimensional entanglement is required for multiparameter estimation. We conclude by illustrating how our method extends naturally to a multipartite splitting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14595 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uncertainty relations between quantum Fisher information and entanglement monotones Du, Shaowei Liu, Shuheng Fadel, Matteo Vitagliano, Giuseppe He, Qiongyi Quantum Physics Entanglement is widely regarded as an essential resource for a number of tasks and can in some cases be quantified by figures of merit related to those tasks. In quantum metrology, this is showcased by the connections between the quantum Fisher information (QFI), providing a bound to the precision, and multipartite entanglement quantifiers such as the entanglement depth. However, a connection between the QFI and entanglement monotones, i.e., functions that do not increase under Local Operations and Classical Communications, has so far remained elusive. In this work, we fill this gap by introducing a family of uncertainty relations that bound bipartite entanglement monotones from below via elements of a quantum Fisher information matrix. To further emphasize the significance of our results, we connect these relations to the achievable precision in multiparameter estimation. Considering a system split into two parts with arbitrary dimension, we also show that, while two-dimensional entanglement is sufficient to estimate a single parameter with maximal precision, genuine high-dimensional entanglement is required for multiparameter estimation. We conclude by illustrating how our method extends naturally to a multipartite splitting. |
| title | Uncertainty relations between quantum Fisher information and entanglement monotones |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2501.14595 |