Optimal probes and error-correction schemes in multi-parameter quantum metrology

Abstract

We derive a necessary and sufficient condition for the possibility of achieving the Heisenberg scaling in general adaptive multi-parameter estimation schemes in presence of Markovian noise. In situations where the Heisenberg scaling is achievable, we provide a semidefinite program to identify the optimal quantum error correcting (QEC) protocol that yields the best estimation precision. We overcome the technical challenges associated with potential incompatibility of the measurement optimally extracting information on different parameters by utilizing the Holevo Cramér-Rao (HCR) bound for pure states. We provide examples of significant advantages offered by our joint-QEC protocols, that sense all the parameters utilizing a single error-corrected subspace, over separate-QEC protocols where each parameter is effectively sensed in a separate subspace.

arXiv comment15+8 pages, 3 figures

References in corpus (57)

• Quantum sensing
• Advances in Quantum Metrology
• Quantum-enhanced measurements: beating the standard quantum limit
• Quantum metrology
• Decoherence Free Subspaces for Quantum Computation
• Quantum metrology with nonclassical states of atomic ensembles
• 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
• Advances in Photonic Quantum Sensing
• The elusive Heisenberg limit in quantum enhanced metrology
• Quantum limits in optical interferometry
• Squeezed states of light and their applications in laser interferometers
• A Quantum Rosetta Stone for Interferometry
• Quantum Theory of Superresolution for Two Incoherent Optical Point Sources
• Quantum Enhanced Multiple Phase Estimation
• Using entanglement against noise in quantum metrology
• Quantum phase estimation with lossy interferometers
• Improved quantum metrology using quantum error-correction
• Compatibility in Multiparameter Quantum Metrology
• Optimal states and almost optimal adaptive measurements for quantum interferometry
• Quantum Error Correction for Metrology
• State estimation for large ensembles
• Achieving the Heisenberg limit in quantum metrology using quantum error correction
• Quantum enhanced estimation of a multi-dimensional field
• Experimental demonstration of a squeezing enhanced power recycled Michelson interferometer for gravitational wave detection
• Distributed Quantum Metrology and the Entangling Power of Linear Networks
• Fundamental Quantum Limit to Waveform Estimation
• A new approach to the Cramer-Rao type bound of the pure state model
• Increasing sensing resolution with error correction
• Multi-parameter estimation beyond Quantum Fisher Information
• Efficient tools for quantum metrology with uncorrelated noise
• Sensitivity Bounds for Multiparameter Quantum Metrology
• Quantum metrology enhanced by repetitive quantum error correction
• Autonomous Quantum Error Correction and Application to Quantum Sensing with Trapped Ions
• Optimal estimation of joint parameters in phase space
• Adaptive quantum metrology under general Markovian noise
• Multiparameter Gaussian Quantum Metrology
• Quantum metrology with full and fast quantum control
• Evaluating the Holevo Cramér-Rao bound for multi-parameter quantum metrology
• Quantum methods for clock synchronization: Beating the standard quantum limit without entanglement
• Quantum local asymptotic normality based on a new quantum likelihood ratio
• Sequential feedback scheme outperforms the parallel scheme for Hamiltonian parameter estimation
• Control-enhanced multiparameter quantum estimation
• Ancilla-free quantum error correction codes for quantum metrology
• $\pi$-Corrected Heisenberg Limit
• Explicit formula for the Holevo bound for two-parameter qubit estimation problem
• Local asymptotic normality in quantum statistics
• Spatial noise filtering through error correction for quantum sensing
• Optimal approximate quantum error correction for quantum metrology
• Stochastic Heisenberg limit: Optimal estimation of a fluctuating phase
• Heisenberg limited metrology using Quantum Error-Correction Codes
• Finite-error metrological bounds on the multi-parameter Hamiltonian estimation
• Fault-tolerant quantum metrology
• True Limits to Precision via Unique Quantum Probe
• Quantum error correction assisted quantum metrology without entanglement
• Fluctuation-enhanced quantum metrology

Cited by in corpus (37)

• A perspective on multiparameter quantum metrology: from theoretical tools to applications in quantum imaging
• Fisher Information in Noisy Intermediate-Scale Quantum Applications
• Optimal Scheme for Quantum Metrology
• Asymptotic theory of quantum channel estimation
• Probe incompatibility in multiparameter noisy quantum metrology
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem
• Imaginarity-free quantum multiparameter estimation
• Bias in error-corrected quantum sensing
• Multiparameter quantum estimation under dephasing noise
• Optimal Universal Quantum Error Correction via Bounded Reference Frames
• Multiple-phase quantum interferometry -- real and apparent gains of measuring all the phases simultaneously
• Quantum non-Gaussianity of multi-phonon states of a single atom
• Multiparameter quantum metrology in the Heisenberg Limit regime: many repetition scenario vs. full optimization
• Practical Limits of Error Correction for Quantum Metrology
• New bounds on adaptive quantum metrology under Markovian noise
• Global Heisenberg scaling in noisy and practical phase estimation
• Achieving metrological limits using ancilla-free quantum error-correcting codes
• Multi-parameter quantum estimation of single- and two-mode pure Gaussian states
• Finding the optimal probe state for multiparameter quantum metrology using conic programming
• Time-local optimal control for parameter estimation in the Gaussian regime
• Time-energy uncertainty relation for noisy quantum metrology
• RLD Fisher Information Bound for Multiparameter Estimation of Quantum Channels
• Metrological symmetries in singular quantum multi-parameter estimation
• Robust quantum metrology with explicit symmetric states
• Optimal distributed multiparameter estimation in noisy environments
• Stabilizer codes for Open Quantum Systems
• Fisher information susceptibility for multiparameter quantum estimation
• Simultaneous estimation of multiple phases in generalised Mach-Zehnder interferometer
• Attainability of the Holevo-Cramér-Rao bound for two-qubit 3D magnetometry
• Critical Quantum Sensing: a tutorial on parameter estimation near quantum phase transitions
• Randomized measurements for multi-parameter quantum metrology
• Efficient tensor networks for control-enhanced quantum metrology
• Selective and noise-resilient wave estimation with quantum sensor networks
• Describing quantum metrology with erasure errors using weight distributions of classical codes
• Optimal and robust error filtration for quantum information processing
• Estimating quantum Markov chains using coherent absorber post-processing and pattern counting estimator
• Gill and Massar type bound for estimation of $SU(2)$ channel