Quantum Metrological Limits via a Variational Approach
arXiv:1207.3307 · doi:10.1103/PhysRevLett.109.190404
Abstract
The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we present an equation for obtaining the quantum Fisher information, which has an explicit dependence on the mathematical description of the noise. This method is applied to obtain a useful analytical bound to the quantum precision in the estimation of phase-shifts under phase diffusion, which shows that the estimation uncertainty cannot be smaller than a noise-dependent constant.
Published Version: 5 pages (including references), 1 figure, typos corrected, and text little bit improved
References in corpus (13)
- Advances in Quantum Metrology
- Quantum-enhanced measurements: beating the standard quantum limit
- A gravitational wave observatory operating beyond the quantum shot-noise limit: Squeezed light in application
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Generalized uncertainty relations: Theory, examples, and Lorentz invariance
- Entanglement-free Heisenberg-limited phase estimation
- Optimal Quantum Phase Estimation
- A Quantum Rosetta Stone for Interferometry
- Quantum phase estimation with lossy interferometers
- Experimental quantum-enhanced estimation of a lossy phase shift
- Optical phase estimation in the presence of phase-diffusion
- Optical interferometry in the presence of large phase diffusion
- Quantum states made to measure
Cited by in corpus (74)
- Quantum metrology with nonclassical states of atomic ensembles
- Quantum limits in optical interferometry
- Quantum speed limit for physical processes
- Open-System Dynamics of Entanglement
- Multi-parameter Quantum Metrology
- A Geometric Perspective on Quantum Parameter Estimation
- Quantum Fisher information of entangled coherent state in the presence of photon losses: exact solution
- Extremal properties of the variance and the quantum Fisher information
- Quantum metrology with full and fast quantum control
- Quantum metrology with open dynamical systems
- Nonlinear quantum metrology of many-body open systems
- Dynamical decoupling leads to improved scaling in noisy quantum metrology
- Quantum probes for the spectral properties of a classical environment
- The quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation
- Review: Quantum Metrology and Sensing with Many-Body Systems
- Characterization of classical Gaussian processes using quantum probes
- Quantum transition-edge detectors
- Quantum Metrological Bounds for Vector Parameter
- Optimal distributed sensing in noisy environments
- Quantum Fisher Information of Entangled Coherent States in a Lossy Mach-Zehnder Interferometer
- Quantum interferometry with binary-outcome measurements in the presence of phase diffusion
- Noisy atomic magnetometry in real time
- Reaching for the quantum limits in the simultaneous estimation of phase and phase diffusion
- Bayesian parameter estimation using Gaussian states and measurements
- Fisher information of a squeezed-state interferometer with a finite photon-number resolution
- Quantum limit for measurement of a weak classical force coupled to a noisy quantum-mechanical oscillator
- Unbounded quantum Fisher information in two-path interferometry with finite photon number
- Zeno dynamics in quantum open systems
- Critical quantum sensing based on the Jaynes-Cummings model with a squeezing drive
- Optimal Quantum Metrology of Distant Black Bodies
- Phase estimation for an SU(1,1) interferometer in the presence of phase diffusion and photon losses
- Valid lower bound for all estimators in quantum parameter estimation
- Precision bounds in noisy quantum metrology
- Bounding the quantum limits of precision for phase estimation with loss and thermal noise
- Quantum sensing of open systems: Estimation of damping constants and temperature
- Approximate decoherence free subspaces for distributed sensing
- Quantum Fisher Information Perspective on Sensing in Anti-PT Symmetric Systems
- Noise limits on two-photon interferometric sensing
- Optical estimation of unitary Gaussian processes without phase reference using Fock states
- Uncertain Quantum Critical Metrology: From Single to Multi Parameter Sensing
- Precision bounds for noisy nonlinear quantum metrology
- Noisy distributed sensing in the Bayesian regime
- Quantum Metrology in Correlated Environments
- Optimal Quantum Thermometry by Dephasing
- Quantum advantage of time-reversed ancilla-based metrology of absorption parameters
- Quantum force estimation in arbitrary non-Markovian Gaussian bath
- Quantum Fisher Information Bounds on Precision Limits of Circular Dichroism
- Phase noise mitigation by a realistic optical parametric oscillator
- Evaluating the quantum Ziv-Zakai bound in noisy environments
- Enhancement of Frequency Estimation by Spatially Correlated Environments
- Improving quantum parameter estimation by monitoring quantum trajectories
- Ultimate phase estimation in a squeezed-state interferometer using photon counters with a finite number resolution
- Quantum metrology in coarsened measurement reference
- Bi-frequency illumination: a quantum-enhanced protocol
- Continuous-variable phase-estimation with unitary and random linear disturbance
- Quantum asymmetry and noisy multi-mode interferometry
- Quantum-enhanced joint estimation of phase and phase diffusion
- Noisy Metrology: A saturable lower bound on quantum Fisher information
- Enhancing precision of atomic clocks by tuning disorder in accessories
- Variational Limits for Phase Precision in Linear Quantum Optical Metrology
- Effects of the reservoir squeezing on the precision of parameter estimation
- Qubit-assisted quantum metrology under a time-reversal strategy
- Bures geodesics and quantum metrology
- Upper bounds on the quantum Fisher Information in the presence of general dephasing
- Quantum Measurement Encoding for Quantum Metrology
- Achieving the Heisenberg limit of metrology via measurement on an ancillary qubit
- Time-adaptive phase estimation
- Joint estimation of phase and phase diffusion for quantum metrology
- Algebraic metrology: Pretty good states and bounds
- Phase Diffusion of Light Immersed In Quantum Tides: Open Quantum System Approach
- Ramsey Scheme Applied to String Theoretical Processes
- Experimental Joint Estimation of Phase and Phase Diffusion via Deterministic Bell Measurements
- Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics
- Precision limit under weak coupling with an ancillary qubit