Minimum Entanglement Protocols for Function Estimation

Abstract

We derive a family of optimal protocols, in the sense of saturating the quantum Cramér-Rao bound, for measuring a linear combination of $d$ field amplitudes with quantum sensor networks, a key subprotocol of general quantum sensor network applications. We demonstrate how to select different protocols from this family under various constraints. Focusing primarily on entanglement-based constraints, we prove the surprising result that highly entangled states are not necessary to achieve optimality in many cases. Specifically, we prove necessary and sufficient conditions for the existence of optimal protocols using at most $k$-partite entanglement. We prove that the protocols which satisfy these conditions use the minimum amount of entanglement possible, even when given access to arbitrary controls and ancilla. Our protocols require some amount of time-dependent control, and we show that a related class of time-independent protocols fail to achieve optimal scaling for generic functions.

arXiv comment21 pages, 1 figure, v3: updated to match published version, includes additional results v2: improved and extended results, fixed technical errors from v1

References in corpus (39)

• Quantum-enhanced measurements: beating the standard quantum limit
• Quantum metrology
• On the Improvement of Frequency Stardards with Quantum Entanglement
• General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
• Entanglement, Non-linear Dynamics, and the Heisenberg Limit
• Quantum metrology from a quantum information science perspective
• Quantum Fisher information matrix and multiparameter estimation
• Generalized uncertainty relations: Theory, examples, and Lorentz invariance
• Entanglement-free Heisenberg-limited phase estimation
• Fisher information and multiparticle entanglement
• Multipartite entanglement and high precision metrology
• The resource theory of quantum reference frames: manipulations and monotones
• Quantum enhanced measurements without entanglement
• Generalized Limits for Single-Parameter Quantum Estimation
• Using entanglement against noise in quantum metrology
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Multi-parameter estimation in networked quantum sensors
• Distributed Quantum Metrology and the Entangling Power of Linear Networks
• Optimal and Secure Measurement Protocols for Quantum Sensor Networks
• Demonstrating Heisenberg-limited unambiguous phase estimation without adaptive measurements
• Robust Calibration of a Universal Single-Qubit Gate-Set via Robust Phase Estimation
• Quantum-limited metrology with product states
• Attaining the ultimate precision limit in quantum state estimation
• $\pi$-Corrected Heisenberg Limit
• Heisenberg-Scaling Measurement Protocol for Analytic Functions with Quantum Sensor Networks
• Quantum state estimation with nuisance parameters
• Quantum sensing networks for the estimation of linear functions
• Detecting metrologically useful asymmetry and entanglement by a few local measurements
• Entanglement is not a critical resource for quantum metrology
• Asymptotic role of entanglement in quantum metrology
• Achieving Heisenberg scaling with maximally entangled states: an analytic upper bound for the attainable root mean square error
• One from many: Estimating a function of many parameters
• Protocols for estimating multiple functions with quantum sensor networks: geometry and performance
• Entangled and sequential quantum protocols with dephasing
• Nuisance parameter problem in quantum estimation theory: General formulation and qubit examples
• Optimal Measurement of Field Properties with Quantum Sensor Networks
• Heisenberg scaling precision in the estimation of functions of parameters
• Distributed quantum phase sensing for arbitrary positive and negative weights

Cited by in corpus (5)

• Quantum-enhanced metrology with network states
• Optimizing Initial State of Detector Sensors in Quantum Sensor Networks
• Optimal distributed multiparameter estimation in noisy environments
• Optimal function estimation with photonic quantum sensor networks
• Quantum Advantage in Distributed Sensing with Noisy Quantum Networks