Maximal quantum Fisher information matrix

Abstract

We study the existence of the maximal quantum Fisher information matrix in multi-parameter quantum estimation, which bounds the ultimate precision limit. We show that when the maximal quantum Fisher information matrix exists, it can be directly obtained from the underlying dynamics. Examples are then provided to demonstrate the usefulness of the maximal quantum Fisher information matrix by deriving various tradeoff relations in multi-parameter quantum estimation and obtaining the bounds for the scalings of the precision limit.

6 pages

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• Fundamental precision bounds for three-dimensional optical localization microscopy with Poisson statistics
• Ultimate precision of multi-parameter quantum magnetometry under the parallel scheme
• Probe incompatibility in multiparameter noisy quantum metrology
• Information geometry under hierarchical quantum measurement
• Optimal joint estimation of multiple Rabi frequencies
• Quantum Fisher Information Perspective on Sensing in Anti-PT Symmetric Systems
• Quantum-limited Localisation and Resolution in Three Dimensions
• Incompatibility measures in multi-parameter quantum estimation under hierarchical quantum measurements
• Bidirectional Teleportation using Fisher Information
• Quantum Fisher Information Bounds on Precision Limits of Circular Dichroism
• Time-energy uncertainty relation for noisy quantum metrology
• Simultaneous Measurement of Multiple Incompatible Observables and Tradeoff in Multiparameter Quantum Estimation
• Randomized measurements for multi-parameter quantum metrology
• Gill and Massar type bound for estimation of $SU(2)$ channel
• Minimal Trade-off and Optimal Measurement for Multiparameter Quantum Estimation