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Quantum estimation for quantum technology
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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.
Forward citations
Cited by 12 Pith papers
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Non-equilibrium quantum thermometry with bosonic samples
Non-Markovian strong coupling in a bosonic probe produces non-monotonic quantum Fisher information with a finite optimal interrogation time for thermometry, while squeezed states give transient gains and strong coupli...
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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.
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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.
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Revealing precision bounds on neutrino oscillation parameters with quantum estimation theory
Quantum Fisher information matrix is derived for neutrino flavor states to obtain Cramér-Rao bounds on oscillation parameters for reactor and accelerator experiments.
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Entanglement response to Temperature in Interacting Two-Qubit Thermal States
Exact expressions for thermal concurrence, its first and second derivatives, and bounds are derived establishing that thermal quantum Fisher information constrains the response and robustness of entanglement to temper...
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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.
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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.
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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.
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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.
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Multiparameter Quantum Estimation and Degeneracy Structure in Three-Flavor Neutrino Oscillations
The quantum Fisher information matrix applied to three-flavor neutrino oscillations reveals that probability degeneracies do not always imply quantum-state indistinguishability.
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Leptonic CP Phase Determination from Fisher Information in NO$\nu$A and T2K
T2K and NOνA extract only a small fraction of the quantum information about δ_CP, with extraction efficiency particularly suppressed near maximal CP violation.
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Electrons on Helium and Entangled Quantum Sensors for Particle Physics
Proposes entangled electron qubits on helium in a double-well trap as a quantum sensor concept for enhanced sensitivity in particle physics.
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