k-designs achieve maximal multi-copy discriminability for pure states when N suffices, mixed states outperform beyond that, and quantum offers quadratic advantage over classical in Bayes capacity terms.
Quantum metrology from a quantum information science perspective
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We summarise important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with Greenberger-Horne-Zeilinger states, Dicke states and singlet states. We calculate the highest precision achievable in these schemes. Then, we present the fundamental notions of quantum metrology, such as shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cramer-Rao bound. Using these, we demonstrate that entanglement is needed to surpass the shot-noise scaling in very general metrological tasks with a linear interferometer. We discuss some applications of the quantum Fisher information, such as how it can be used to obtain a criterion for a quantum state to be a macroscopic superposition. We show how it is related to the the speed of a quantum evolution, and how it appears in the theory of the quantum Zeno effect. Finally, we explain how uncorrelated noise limits the highest achievable precision in very general metrological tasks.
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UNVERDICTED 6representative citing papers
Presents complex versions of Fisher information matrices and Cramér-Rao bounds for quantum estimation depending on complex parameters.
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.
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.
The quantum Fisher information matrix applied to three-flavor neutrino oscillations reveals that probability degeneracies do not always imply quantum-state indistinguishability.
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.
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The most discriminable quantum states in the multicopy regime
k-designs achieve maximal multi-copy discriminability for pure states when N suffices, mixed states outperform beyond that, and quantum offers quadratic advantage over classical in Bayes capacity terms.
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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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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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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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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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Entanglement Certification $-$ From Theory to Experiment
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.