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

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.

arXiv comment26 pages, 10 figures. Accepted version in Quantum Journal

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• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Symmetric quantum states: a review of recent progress
• Introduction to quantum entanglement in many-body systems
• Certification of quantum state functions under partial information
• Inherent quantum resources in stationary spin chains
• Topological quantum thermometry
• Critical Quantum Sensing: a tutorial on parameter estimation near quantum phase transitions
• Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
• Thresholded Quantum Sensing with a Frustrated Kitaev Trimer
• Minimal-noise estimation of noncommuting rotations of a spin