Quantum metrology with imperfect measurements

Abstract

The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving $N$ probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections -- with global control operations, the ideal sensitivity (e.g.~the Heisenberg scaling) can always be recovered in the asymptotic $N$ limit, while with local control operations the quantum-enhancement of sensitivity is constrained to a constant factor. We illustrate our findings with an example of NV-centre magnetometry, as well as schemes involving spin-$1/2$ probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision.

v2. 33 pages, 14 figures. Comments are welcome

References in corpus (10)

• High-sensitivity diamond magnetometer with nanoscale resolution
• Squeezing and entanglement in a Bose-Einstein condensate
• The Quantum Chernoff Bound
• Quantum sensing with arbitrary frequency resolution
• The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
• Quantum metrology with imperfect states and detectors
• Weak Value Amplification Can Outperform Conventional Measurement in the Presence of Detector Saturation
• Approaching quantum-limited metrology with imperfect detectors by using weak-value amplification
• Quantum Metrology: Extended Convexity of Quantum Fisher Information
• Quantum Noise-to-Sensibility Ratio

Cited by in corpus (32)

• Entanglement-enhanced quantum metrology: from standard quantum limit to Heisenberg limit
• Multiparameter estimation perspective on non-Hermitian singularity-enhanced sensing
• Measurement noise susceptibility in quantum estimation
• Optimal protocols for quantum metrology with noisy measurements
• Inter-species spin-noise correlations in hot atomic vapors
• Squeezed superradiance enables robust entanglement-enhanced metrology even with highly imperfect readout
• Theory of Compression Channels for Postselected Quantum Metrology
• Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach
• Limits of noisy quantum metrology with restricted quantum controls
• Stochastic waveform estimation at the fundamental quantum limit
• Approaching maximal precision of Hong-Ou-Mandel interferometry with non-perfect visibility
• Multiparameter estimation for qubit states with collective measurements: a case study
• Fisher information susceptibility for multiparameter quantum estimation
• Gottesman-Kitaev-Preskill encoding in continuous modal variables of single photons
• Generalized squeezing as a witness
• Enhancing precision of atomic clocks by tuning disorder in accessories
• Assessing small accelerations using a bosonic Josephson junction
• Beating the Ramsey limit on sensing with deterministic qubit control
• Quantum Limits on Localizing Point Objects against a Uniformly Bright Disk
• Efficient tensor networks for control-enhanced quantum metrology
• Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
• Adaptive, symmetry-informed Bayesian metrology for precise quantum technology measurements
• Purely quantum memory in closed systems observed via imperfect measurements
• Optimal Local Measurements in Single-Parameter Quantum Metrology
• Informationally Complete Distributed Metrology Without a Shared Reference Frame
• Noisy initial-state qubit-channel metrology with additional undesirable noisy evolution
• A physical noise model for quantum measurements
• Fundamental limits to contrast reversal of survival probability correlations
• Detecting Entanglement by State Preparation and Local Measurements
• Extending the dynamic range in quantum frequency estimation with sequential weak measurements
• Quantum Metrology under Coarse-Grained Measurement
• Towards Robust Optimal Measurements Against Noise in Quantum Metrology