Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach

• URL: http://arxiv.org/abs/2306.12711v3
• Date: Thu, 19 Oct 2023 10:35:16 GMT
• Title: Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach
• Authors: Guillem M\"uller-Rigat, Anubhav Kumar Srivastava, Stanis{\l}aw Kurdzia{\l}ek, Grzegorz Rajchel-Mieldzio\'c, Maciej Lewenstein and Ir\'en\'ee Fr\'erot
• Abstract summary: We introduce a semidefinite programming algorithm to find the minimal quantum Fisher information compatible with an arbitrary dataset of mean values. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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