k-designs achieve maximal discriminability for pure states in multi-copy minimum-error discrimination; mixed states outperform for larger ensembles, with quantum offering quadratic advantage over classical.
Tóth and I
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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 5representative 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.
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 discriminability for pure states in multi-copy minimum-error discrimination; mixed states outperform for larger ensembles, with quantum offering quadratic advantage over classical.
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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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Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.