Estimation of gradients in quantum metrology
arXiv:1703.09123 · doi:10.1103/PhysRevA.96.042319
Abstract
We develop a general theory to estimate magnetic field gradients in quantum metrology. We consider a system of particles distributed on a line whose internal degrees of freedom interact with a magnetic field. Usually gradient estimation is based on precise measurements of the magnetic field at two different locations, performed with two independent groups of particles. This approach, however, is sensitive to fluctuations of the off-set field determining the level-splitting of the particles and results in collective dephasing. In this work we use the framework of quantum metrology to assess the maximal accuracy for gradient estimation. For arbitrary positioning of particles, we identify optimal entangled and separable states allowing the estimation of gradients with the maximal accuracy, quantified by the quantum Fisher information. We also analyze the performance of states from the decoherence-free subspace (DFS), which are insensitive to the fluctuations of the magnetic offset field. We find that these states allow to measure a gradient directly, without the necessity of estimating the magnetic offset field. Moreover, we show that DFS states attain a precision for gradient estimation comparable to the optimal entangled states. Finally, for the above classes of states we find simple and feasible measurements saturating the quantum Cramér-Rao bound.
arXiv comment22 pages, 8 figures. See also the related work by I. Apellaniz et al. arXiv: 1703.09056 (2017)
References in corpus (35)
- Quantum metrology
- Decoherence Free Subspaces for Quantum Computation
- 14-qubit entanglement: creation and coherence
- Quantum computation with ions in thermal motion
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Demonstration of a neutral atom controlled-NOT quantum gate
- Reference frames, superselection rules, and quantum information
- Quantum metrology from a quantum information science perspective
- The elusive Heisenberg limit in quantum enhanced metrology
- Entanglement of two individual neutral atoms using Rydberg blockade
- Quantum limits in optical interferometry
- Quantum Metrology for Gravitational Wave Astronomy
- Ion-trap quantum logic using long-wavelength radiation
- Compatibility in Multiparameter Quantum Metrology
- Blueprint for a microwave trapped-ion quantum computer
- Optimal states and almost optimal adaptive measurements for quantum interferometry
- Sub-nanometer resolution in three-dimensional magnetic-resonance imaging of individual dark spins
- Analysis of dephasing mechanisms in a standing wave dipole trap
- True precision limits in quantum metrology
- Ultrasensitive Magnetometer Using a Single Atom
- Sensing electric and magnetic fields with Bose-Einstein Condensates
- Quantum frequency estimation with trapped ions and atoms
- Random bosonic states for robust quantum metrology
- Macroscopic singlet states for gradient magnetometry
- Scalable Architecture for Quantum Information Processing with Atoms in Optical Micro-Structures
- Quantum Phase Estimation with Entangled Photons produced by Parametric Down Conversion
- Quantum dynamics of trapped ions in a dynamic field gradient using dressed states
- Phase-noise protection in quantum-enhanced differential interferometry
- Fitting magnetic field gradient with Heisenberg-scaling accuracy
- Networked quantum sensing
- Optimized parameter estimation in the presence of collective phase noise
- Entangled states of trapped ions allow measuring the magnetic field gradient of a single atomic spin
- A single ion as a shot noise limited magnetic field gradient probe
- Noise assisted Ramsey interferometry
- Characterizing the width of entanglement
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- Tensor-Network Approach for Quantum Metrology in Many-Body Quantum Systems
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- Hybrid quantum-classical approach to enhanced quantum metrology
- Nuisance parameter problem in quantum estimation theory: General formulation and qubit examples
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