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.
5+3 pages, 3 figures
References in corpus (17)
- Quantum metrology from a quantum information science perspective
- Quantum Optical Metrology -- The Lowdown on High-N00N States
- Quantum Metrology for Gravitational Wave Astronomy
- Using entanglement against noise in quantum metrology
- Sub-millihertz magnetic spectroscopy with a nanoscale quantum sensor
- 'Designer atoms' for quantum metrology
- Magnetic field sensing beyond the standard quantum limit using 10-spin NOON states
- Entangled Fock states for Robust Quantum Optical Metrology, Imaging, and Sensing
- Qubit metrology and decoherence
- Quantum Variational Optimization of Ramsey Interferometry and Atomic Clocks
- Loss-Induced Limits to Phase Measurement Precision with Maximally Entangled States
- 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