Entanglement-enhanced quantum metrology: from standard quantum limit to Heisenberg limit

Entanglement-enhanced quantum metrology: from standard quantum limit to Heisenberg limit

5 June 2024 | Jiahao Huang, Min Zhuang, and Chaohong Lee
Entanglement-enhanced quantum metrology explores the use of quantum entanglement to improve measurement precision beyond the standard quantum limit (SQL) and approach the Heisenberg limit (HL). By preparing particles in suitable entangled states, quantum sensors can achieve higher precision in measuring physical quantities such as magnetic fields, frequencies, and accelerations. This review discusses the fundamental principles, experimental progress, and potential applications of entanglement-enhanced quantum metrology. Quantum parameter estimation involves determining unknown parameters using quantum mechanics and estimation theory. Quantum interferometry is a common method for high-precision parameter estimation, where quantum probes accumulate phase information relevant to the measured quantity. The SQL limits measurement precision to $ \Delta\theta \propto N^{-1/2} $, while entangled states can surpass this limit, achieving $ \Delta\theta \propto N^{-1} $, the HL. Key entangled states used in quantum metrology include spin-squeezed states, twin-Fock states, and spin-cat states. These states are prepared in various quantum systems such as cold atoms, trapped ions, and Bose-Einstein condensates. Effective interrogation and readout techniques, including nonlinear detection and interaction-based methods, are essential for extracting information from entangled states. Applications of entanglement-enhanced quantum sensors include atomic clocks, magnetometers, gravimeters, and gyroscopes. These sensors offer high precision and sensitivity, enabling tasks such as maintaining communication networks, real-time brain imaging, and monitoring geological activity. The integration of quantum control with entanglement is expected to significantly advance entanglement-enhanced sensing technologies. This review provides a comprehensive overview of entanglement-enhanced quantum metrology, covering its fundamental principles, experimental realization, and wide range of potential applications. It highlights the importance of quantum entanglement in achieving higher measurement precision and discusses the strategies for quantum metrology, including classical-classical (CC), classical-quantum (CQ), quantum-classical (QC), and quantum-quantum (QQ) strategies. The ultimate precision limits for these strategies are discussed, with the QQ strategy providing the best performance. The review also introduces typical multi-particle entangled states and their preparation in various quantum systems.Entanglement-enhanced quantum metrology explores the use of quantum entanglement to improve measurement precision beyond the standard quantum limit (SQL) and approach the Heisenberg limit (HL). By preparing particles in suitable entangled states, quantum sensors can achieve higher precision in measuring physical quantities such as magnetic fields, frequencies, and accelerations. This review discusses the fundamental principles, experimental progress, and potential applications of entanglement-enhanced quantum metrology. Quantum parameter estimation involves determining unknown parameters using quantum mechanics and estimation theory. Quantum interferometry is a common method for high-precision parameter estimation, where quantum probes accumulate phase information relevant to the measured quantity. The SQL limits measurement precision to $ \Delta\theta \propto N^{-1/2} $, while entangled states can surpass this limit, achieving $ \Delta\theta \propto N^{-1} $, the HL. Key entangled states used in quantum metrology include spin-squeezed states, twin-Fock states, and spin-cat states. These states are prepared in various quantum systems such as cold atoms, trapped ions, and Bose-Einstein condensates. Effective interrogation and readout techniques, including nonlinear detection and interaction-based methods, are essential for extracting information from entangled states. Applications of entanglement-enhanced quantum sensors include atomic clocks, magnetometers, gravimeters, and gyroscopes. These sensors offer high precision and sensitivity, enabling tasks such as maintaining communication networks, real-time brain imaging, and monitoring geological activity. The integration of quantum control with entanglement is expected to significantly advance entanglement-enhanced sensing technologies. This review provides a comprehensive overview of entanglement-enhanced quantum metrology, covering its fundamental principles, experimental realization, and wide range of potential applications. It highlights the importance of quantum entanglement in achieving higher measurement precision and discusses the strategies for quantum metrology, including classical-classical (CC), classical-quantum (CQ), quantum-classical (QC), and quantum-quantum (QQ) strategies. The ultimate precision limits for these strategies are discussed, with the QQ strategy providing the best performance. The review also introduces typical multi-particle entangled states and their preparation in various quantum systems.
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[slides and audio] Entanglement-enhanced quantum metrology%3A From standard quantum limit to Heisenberg limit