Universal time scalings of sensitivity in Markovian quantum metrology
arXiv:2404.03954 · doi:10.1103/PhysRevA.111.L020403
Abstract
Assuming Markovian time evolution of a quantum sensing system, we study the general characterization of the optimal sensitivity scalings with time, under most general quantum control protocols. We allow the estimated parameter to influence both the Hamiltonian as well as the dissipative part of the quantum master equation and focus on the asymptotic-time along with the short-time sensitivity scalings. We find that via simple algebraic conditions (in terms of the Hamiltonian, the jump operators as well as their parameter derivatives), one can characterize the four classes of metrological models that represent: quadratic-linear, quadratic-quadratic, linear-linear and linear-quadratic time scalings. We also investigate the relevant time scales on which the transition between the two regimes appears. Additionally, we provide universal numerical methods to obtain quantitative bounds on sensitivity that are the tightest that exist in the literature. Simplicity and universality of our results make it suitable for diverse applications in quantum metrology.
arXiv comment5+3 pages, 3 figures
References in corpus (49)
- Quantum entanglement
- Quantum sensing
- Advances in Quantum Metrology
- Quantum metrology
- Quantum Coherence as a Resource
- Quantum metrology with nonclassical states of atomic ensembles
- Quantum Resource Theories
- On the Improvement of Frequency Stardards with Quantum Entanglement
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Quantum metrology from a quantum information science perspective
- Quantum Optical Metrology -- The Lowdown on High-N00N States
- Advances in Photonic Quantum Sensing
- The elusive Heisenberg limit in quantum enhanced metrology
- Quantum Metrology in Non-Markovian Environments
- A Quantum Rosetta Stone for Interferometry
- Quantum enhanced measurements without entanglement
- Quantum Metrology for Gravitational Wave Astronomy
- First Long-Term Application of Squeezed States of Light in a Gravitational-Wave Observatory
- Using entanglement against noise in quantum metrology
- Sub-millihertz magnetic spectroscopy with a nanoscale quantum sensor
- 'Designer atoms' for quantum metrology
- Quantum phase estimation with lossy interferometers
- Improved quantum metrology using quantum error-correction
- Magnetic field sensing beyond the standard quantum limit using 10-spin NOON states
- Quantum Error Correction for Metrology
- Achieving the Heisenberg limit in quantum metrology using quantum error correction
- Entangled Fock states for Robust Quantum Optical Metrology, Imaging, and Sensing
- Increasing sensing resolution with error correction
- The ultimate precision limits for noisy frequency estimation
- Quantum metrology enhanced by repetitive quantum error correction
- Adaptive quantum metrology under general Markovian noise
- 0.75 atoms improve the clock signal of 10,000 atoms
- Qubit metrology and decoherence
- Quantum metrology with full and fast quantum control
- Ultimate Precision of Adaptive Noise Estimation
- Effects of photon losses on phase estimation near the Heisenberg limit using coherent light and squeezed vacuum
- Quantum Variational Optimization of Ramsey Interferometry and Atomic Clocks
- Loss-Induced Limits to Phase Measurement Precision with Maximally Entangled States
- Noisy quantum metrology enhanced by continuous nondemolition measurement
- Ultimate precision of multi-parameter quantum magnetometry under the parallel scheme
- Asymptotic theory of quantum channel estimation
- Quantum states made to measure
- Heisenberg-limited noisy atomic clock using a hybrid coherent and squeezed states protocol
- QuanEstimation: An open-source toolkit for quantum parameter estimation
- Error-Mitigated Quantum Metrology via Virtual Purification
- Using adaptiveness and causal superpositions against noise in quantum metrology
- Optimal nonequilibrium thermometry in Markovian environments
- New bounds on adaptive quantum metrology under Markovian noise
- Quantum metrology using quantum combs and tensor network formalism