Quantum estimation for quantum technology
read the original abstract
Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine the value of these quantities should resort to indirect measurements and thus corresponds to a parameter estimation problem whose solution, i.e the determination of the most precise estimator, unavoidably involves an optimization procedure. We review local quantum estimation theory and present explicit formulas for the symmetric logarithmic derivative and the quantum Fisher information of relevant families of quantum states. Estimability of a parameter is defined in terms of the quantum signal-to-noise ratio and the number of measurements needed to achieve a given relative error. The connections between the optmization procedure and the geometry of quantum statistical models are discussed. Our analysis allows to quantify quantum noise in the measurements of non observable quantities and provides a tools for the characterization of signals and devices in quantum technology.
This paper has not been read by Pith yet.
Forward citations
Cited by 6 Pith papers
-
Precision limits for time-dependent quantum metrology under Markovian noise
Derives differential upper bounds on quantum Fisher information for time-dependent metrology under Markovian noise and proves universal long-time scaling laws saturated by quantum error correction.
-
Probabilistic quantum algorithm for Lyapunov equations and matrix inversion
Probabilistic quantum algorithm prepares mixed states proportional to Lyapunov equation solutions and matrix inverses using oracles for input matrices and a deterministic stopping rule.
-
Entanglement Requirements for Coherent Enhancement in Detectors
Coherent enhancement in detectors is quantitatively constrained by single-mode entanglement entropy, with general bounds on scaling with system size that interpolate between incoherent and fully coherent regimes.
-
Ultimate sensitivity of multiparameter estimation in quantum sensing with undetected photons
Quantum sensing with undetected photons achieves optimal multiparameter estimation precision using a single phase shift and multipass count scaling as the inverse log of transmission.
-
Leggett-Garg Inequality Violations Bound Quantum Fisher Information
Leggett-Garg inequality violations yield lower bounds on quantum Fisher information in stationary pure and thermal states, serving as a witness for many-body quantum coherence.
-
Complex Field Formulation of the Quantum Estimation Theory
Presents complex versions of Fisher information matrices and Cramér-Rao bounds for quantum estimation depending on complex parameters.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.