Tensor-Network Approach for Quantum Metrology in Many-Body Quantum Systems

Abstract

Identification of the optimal quantum metrological protocols in realistic many particle quantum models is in general a challenge that cannot be efficiently addressed by the state-of-the-art numerical and analytical methods. Here we provide a comprehensive framework exploiting matrix product operators (MPO) type tensor networks for quantum metrological problems. Thanks to the fact that the MPO formalism allows for an efficient description of short-range spatial and temporal noise correlations, the maximal achievable estimation precision in such models, as well as the optimal probe states in previously inaccessible regimes can be identified. Moreover, the application of infinite MPO (iMPO) techniques allows for a direct and efficient determination of the asymptotic precision of optimal protocols in the limit of infinite particle numbers. We illustrate the potential of our framework in terms of an atomic clock stabilization (temporal noise correlation) example as well as for magnetic field sensing in the presence of locally correlated magnetic field fluctuations (spatial noise correlations). As a byproduct, the developed methods for calculating the quantum Fisher information via MPOs may be used to calculate the fidelity susceptibility - a parameter widely used in many-body physics to study phase transitions.

24 pages

References in corpus (6)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Efficient quantum state tomography
• Using entanglement against noise in quantum metrology
• Characterizing topological order by studying the ground states of an infinite cylinder
• Finite temperature fidelity susceptibility for one-dimensional quantum systems

Cited by in corpus (34)

• Optimal metrology with programmable quantum sensors
• Multi-parameter estimation beyond Quantum Fisher Information
• A variational toolbox for quantum multi-parameter estimation
• Quantum Variational Optimization of Ramsey Interferometry and Atomic Clocks
• Quantum Semiparametric Estimation
• Asymptotic theory of quantum channel estimation
• QuanEstimation: An open-source toolkit for quantum parameter estimation
• Probe incompatibility in multiparameter noisy quantum metrology
• One- and two-axis squeezing via laser coupling in an atomic Fermi-Hubbard model
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem
• Efficient Information Retrieval for Sensing via Continuous Measurement
• Non-Markovian Sensing of a Quantum Reservoir
• Steering-enhanced quantum metrology using superpositions of noisy phase shifts
• Generation of Photonic Matrix Product States with Rydberg Atomic Arrays
• Bound entangled singlet-like states for quantum metrology
• Threshold for a discrete-variable sensor of quantum reservoirs
• Criticality-enhanced quantum sensor at finite temperature
• Classification and reconstruction of optical quantum states with deep neural networks
• Time-energy uncertainty relation for noisy quantum metrology
• A tensor network approach to sensing quantum light-matter interactions
• Optimizing one-axis twists for variational Bayesian quantum metrology
• TNQMetro: Tensor-network based package for efficient quantum metrology computations
• Heisenberg-limited metrology with perturbing interactions
• Generation of photonic tensor network states with Circuit QED
• Quantum-enhanced joint estimation of phase and phase diffusion
• Universal bounds for quantum metrology in the presence of correlated noise
• Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains at Finite Temperature: Exact Results
• Efficient tensor networks for control-enhanced quantum metrology
• Quantum Cramer-Rao Precision Limit of Noisy Continuous Sensing
• Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
• Quantum Fisher information from tensor network integration of Lyapunov equation
• QMetro++ -- Python optimization package for large scale quantum metrology with customized strategy structures
• Detecting Entanglement by State Preparation and Local Measurements
• Simulation of the Dissipative Dynamics of Strongly Interacting NV Centers with Tensor Networks