Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 47, Issue 42, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/47/42/424006
Keywords
quantum metrology; entanglement; Fisher information; spin squeezing
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Funding
- ERC StG GEDENTQOPT at the University of the Basque Country UPV/EHU
- EU (ERC)
- Spanish MINECO [FIS2009-12773-C02-02, FIS2012-36673-C03-03]
- Basque Government [IT4720-10]
- National Research Fund of Hungary OTKA [K83858]
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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 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 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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