Quantum metrology from a quantum information science perspective

By Géza Tóth, Iagoba Apellaniz. 2014

908 citations recorded by the source corpus.

We summarize 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 Cramér–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 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. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/490b50a64a58c3769d5fe8bc0e5ec9c78dc6927b

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Entanglement certification from theory to experiment (2018, background): “Finally, entanglement can be understood as a means of bringing about speed-ups [52– 54], parallelisation [55], and even flexibility [56] in quantum metrology [57].”
Quantum Fisher information matrix and multiparameter estimation (2019, methodology): “trics on quantum states indicates that the QFIM can be used to quantify the evolution time. As a matter of fact, the QFI and the QFIM have been used to bound the quantum speed limit in recent studies [7,36,75,76]. For a unitary evolution, U = exp( iHt), to steer a state away from the initial positio”
Quantum metrology with nonclassical states of atomic ensembles (2016, background): “In the literature, different definitions of spin squeezing for collective angular momentum operators can be found (Ma et al., 2011; Tóth and Apellaniz, 2014).”
Macroscopic quantum states: Measures, fragility, and implementations (2017, background): “We now turn to quantum metrology (Giovannetti et al., 2011; Pezzè et al., 2016; Tóth and Apellaniz, 2014) as a potential application of large-scale quantum systems.”
Geometry of quantum phase transitions (2019, background): “Exploring this possibility plays a pivotal role in the current development of quantum technology [306, 307, 308, 309, 310, 311, 312, 313, 314, 315].”
Bounds on the capacity and power of quantum batteries (2018, background): “[16] and [17] for a review in the context of quantum information and quantum optics, respectively.”
Quantum-enhanced measurements without entanglement (2017, background): “The literature on the topic of quantum metrology is vast and for a general introduction we refer to the available reviews (Degen et al., 2016; Giovannetti et al., 2006; Paris, 2009; Pezzè and Smerzi, 2014; Pezzè et al., 2016; Tóth and Apellaniz, 2014; Wiseman and Milburn, 2009).”