Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach
We introduce a semidefinite programming algorithm to find the minimal quantum Fisher information compatible with an arbitrary dataset of mean values. This certification task allows one to quantify the resource content of a quantum system for metrology applications without complete knowledge of the q...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-10-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-10-24-1152/pdf/ |
| _version_ | 1827784839395278848 |
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| author | Guillem Müller-Rigat Anubhav Kumar Srivastava Stanisław Kurdziałek Grzegorz Rajchel-Mieldzioć Maciej Lewenstein Irénée Frérot |
| author_facet | Guillem Müller-Rigat Anubhav Kumar Srivastava Stanisław Kurdziałek Grzegorz Rajchel-Mieldzioć Maciej Lewenstein Irénée Frérot |
| author_sort | Guillem Müller-Rigat |
| collection | DOAJ |
| description | We introduce a semidefinite programming algorithm to find the minimal quantum Fisher information compatible with an arbitrary dataset of mean values. This certification task allows one to quantify the resource content of a quantum system for metrology applications without complete knowledge of the quantum state. We implement the algorithm to study quantum spin ensembles. We first focus on Dicke states, where our findings challenge and complement previous results in the literature. We then investigate states generated during the one-axis twisting dynamics, where in particular we find that the metrological power of the so-called multi-headed cat states can be certified using simple collective spin observables, such as fourth-order moments for small systems, and parity measurements for arbitrary system sizes. |
| first_indexed | 2024-03-11T16:09:47Z |
| format | Article |
| id | doaj.art-f96c0428e9ed4e769179273c4ec52492 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-11T16:09:47Z |
| publishDate | 2023-10-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-f96c0428e9ed4e769179273c4ec524922023-10-24T16:02:52ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-10-017115210.22331/q-2023-10-24-115210.22331/q-2023-10-24-1152Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approachGuillem Müller-RigatAnubhav Kumar SrivastavaStanisław KurdziałekGrzegorz Rajchel-MieldzioćMaciej LewensteinIrénée FrérotWe introduce a semidefinite programming algorithm to find the minimal quantum Fisher information compatible with an arbitrary dataset of mean values. This certification task allows one to quantify the resource content of a quantum system for metrology applications without complete knowledge of the quantum state. We implement the algorithm to study quantum spin ensembles. We first focus on Dicke states, where our findings challenge and complement previous results in the literature. We then investigate states generated during the one-axis twisting dynamics, where in particular we find that the metrological power of the so-called multi-headed cat states can be certified using simple collective spin observables, such as fourth-order moments for small systems, and parity measurements for arbitrary system sizes.https://quantum-journal.org/papers/q-2023-10-24-1152/pdf/ |
| spellingShingle | Guillem Müller-Rigat Anubhav Kumar Srivastava Stanisław Kurdziałek Grzegorz Rajchel-Mieldzioć Maciej Lewenstein Irénée Frérot Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach Quantum |
| title | Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach |
| title_full | Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach |
| title_fullStr | Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach |
| title_full_unstemmed | Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach |
| title_short | Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach |
| title_sort | certifying the quantum fisher information from a given set of mean values a semidefinite programming approach |
| url | https://quantum-journal.org/papers/q-2023-10-24-1152/pdf/ |
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