Minimal Trade-off and Optimal Measurement for Multiparameter Quantum Estimation
arXiv:2605.23514 · doi:10.1103/dvj7-9thf
Abstract
A fundamental challenge in multiparameter quantum estimation arises from the incompatibility of optimal measurements for different parameters, leading to intricate precision trade-offs that obscure the understanding of ultimate quantum limits. Here, we present an approach that precisely quantifies these trade-offs for an arbitrary number of parameters encoded in pure quantum states. Our approach not only derives tight analytical bounds for the trade-offs induced by measurement incompatibility but also provides a systematic methodology to design optimal measurement strategies that saturate these limits. To demonstrate the practical significance of our findings, we apply our framework to quantum radar and obtain a refined Arthurs-Kelly relation that characterizes the ultimate performance for the simultaneous estimation of range and velocity with any given amount of entanglement. This showcases the transformative potential of our findings for a wide range of applications in quantum metrology, sensing, and beyond.
This is a companion paper to arXiv:2504.09490
References in corpus (53)
- Quantum Fisher information matrix and multiparameter estimation
- Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
- Compatibility in Multiparameter Quantum Metrology
- State estimation for large ensembles
- Multi-parameter Quantum Metrology
- Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements
- A Geometric Perspective on Quantum Parameter Estimation
- A perspective on multiparameter quantum metrology: from theoretical tools to applications in quantum imaging
- A new approach to the Cramer-Rao type bound of the pure state model
- Optimal measurements for simultaneous quantum estimation of multiple phases
- Multi-parameter estimation beyond Quantum Fisher Information
- On quantumness in multi-parameter quantum estimation
- How well can one jointly measure two incompatible observables on a given quantum state?
- A tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry
- Prior information: how to circumvent the standard joint-measurement uncertainty relation
- Local asymptotic normality for finite dimensional quantum systems
- Evaluating the Holevo Cramér-Rao bound for multi-parameter quantum metrology
- Quantum local asymptotic normality based on a new quantum likelihood ratio
- Attaining the ultimate precision limit in quantum state estimation
- Uncertainty Relations for Joint Measurements of Noncommuting Observables
- Control-enhanced multiparameter quantum estimation
- Quantum radar
- Physical content of Heisenberg's uncertainty relation: Limitation and reformulation
- Quantum-enhanced metrology for multiple phase estimation with noise
- Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation
- Explicit formula for the Holevo bound for two-parameter qubit estimation problem
- Tight bounds on the simultaneous estimation of incompatible parameters
- Approaching optimal entangling collective measurements on quantum computing platforms
- Ultimate precision of multi-parameter quantum magnetometry under the parallel scheme
- Quantum ranging with Gaussian entanglement
- Entangling measurements for multiparameter estimation with two qubits
- Ultimate accuracy limit of quantum pulse-compression ranging
- Efficient computation of the Nagaoka--Hayashi bound for multi-parameter estimation with separable measurements
- Optimal Strategies of Quantum Metrology with a Strict Hierarchy
- Using adaptiveness and causal superpositions against noise in quantum metrology
- Quantum Metrological Bounds for Vector Parameter
- Incompatibility in Quantum Parameter Estimation
- Universally Fisher-Symmetric Informationally Complete Measurements
- Quantum-enhanced Doppler lidar
- Deriving tight error-trade-off relations for approximate joint measurements of incompatible quantum observables
- On the quantumness of multiparameter estimation problems for qubit systems
- Quantum-limited estimation of range and velocity
- Maximal quantum Fisher information matrix
- Optimal joint estimation of multiple Rabi frequencies
- Information geometry under hierarchical quantum measurement
- Measurement noise susceptibility in quantum estimation
- Improved Error-Tradeoff and Error-Disturbance Relations
- Incompatibility measures in multi-parameter quantum estimation under hierarchical quantum measurements
- Heisenberg-Limited Quantum Lidar for Joint Range and Velocity Estimation
- Heisenberg's uncertainty relation: Violation and reformulation
- Overcoming Quantum Metrology Singularity through Sequential Measurements
- Simultaneous Measurement of Multiple Incompatible Observables and Tradeoff in Multiparameter Quantum Estimation
- Metrological symmetries in singular quantum multi-parameter estimation