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

TL;DR

This paper presents a semidefinite programming method to certify the quantum Fisher information from limited measurement data, enabling resource quantification in quantum metrology without full state knowledge.

Contribution

It introduces a novel SDP-based algorithm for certifying quantum Fisher information from mean values, applicable to various quantum states and measurements.

Findings

Certified metrological power of Dicke states and multi-headed cat states.

Identified simple measurement schemes for certifying quantum resources.

Challenged and extended previous results on quantum Fisher information.

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.