Achieving Heisenberg scaling with maximally entangled states: an analytic upper bound for the attainable root mean square error
arXiv:2007.02994 · doi:10.1103/PhysRevA.102.042613
Abstract
In this paper we explore the possibility of performing Heisenberg limited quantum metrology of a phase, without any prior, by employing only maximally entangled states. Starting from the estimator introduced by Higgins et al. in New J. Phys. 11, 073023 (2009), the main result of this paper is to produce an analytical upper bound on the associated Mean Squared Error which is monotonically decreasing as a function of the square of the number of quantum probes used in the process. The analysed protocol is non-adaptive and requires in principle (for distinguishable probes) only separable measurements. We explore also metrology in presence of a limitation on the entanglement size and in presence of loss.
arXiv comment20 pages, 14 figures. Corrected typos
References in corpus (37)
- Quantum sensing
- Advances in Quantum Metrology
- Quantum-enhanced measurements: beating the standard quantum limit
- Quantum metrology
- Optical Magnetometry
- Quantum metrology with nonclassical states of atomic ensembles
- Quantum Algorithms Revisited
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Quantum metrology from a quantum information science perspective
- Generalized uncertainty relations: Theory, examples, and Lorentz invariance
- Entanglement-free Heisenberg-limited phase estimation
- Quantum limits in optical interferometry
- Optimal Quantum Phase Estimation
- Quantum enhanced measurements without entanglement
- Quantum noise limited and entanglement-assisted magnetometry
- Magnetic sensitivity beyond the projection noise limit by spin squeezing
- Optimal states and almost optimal adaptive measurements for quantum interferometry
- Amplitude estimation without phase estimation
- Machine Learning for Precise Quantum Measurement
- How to perform the most accurate possible phase measurements
- Quantum optical technologies for metrology, sensing and imaging
- Entanglement-assisted atomic clock beyond the projection noise limit
- Demonstrating Heisenberg-limited unambiguous phase estimation without adaptive measurements
- Heisenberg-limited atom clocks based on entangled qubits
- Robust Calibration of a Universal Single-Qubit Gate-Set via Robust Phase Estimation
- -Corrected Heisenberg Limit
- Experimental optical phase measurement approaching the exact Heisenberg limit
- Parameter Estimation with Mixed-State Quantum Computation
- Quantum metrology: why entanglement?
- Experimental demonstration of cheap and accurate phase estimation
- Adaptive Measurements in the Optical Quantum Information Laboratory
- Entangled and sequential quantum protocols with dephasing
- Universal quantum magnetometry with spin states at equilibrium
- Valid lower bound for all estimators in quantum parameter estimation
- Feedback Ansatz for Adaptive-Feedback Quantum Metrology Training with Machine Learning
- Phase estimation with photon number constraint
- Usefulness of an enhanced Kitaev phase-estimation algorithm in quantum metrology and computation
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