Entanglement, nonlinear dynamics, and the heisenberg limit.

  title={Entanglement, nonlinear dynamics, and the heisenberg limit.},
  author={Luca Pezz{\`e} and Augusto Smerzi},
  journal={Physical review letters},
  volume={102 10},
We show that quantum Fisher information provides a sufficient condition to recognize multiparticle entanglement in an N qubit state. The same criterion gives a necessary and sufficient condition for sub-shot-noise phase sensitivity in the estimation of a collective rotation angle theta. The analysis therefore singles out the class of entangled states which are useful to overcome classical phase sensitivity in metrology and sensors. We finally study the creation of useful entangled states by the… 

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Quantum detection and estimation theory
A review. Quantum detection theory is a reformulation, in quantum-mechanical terms, of statistical decision theory as applied to the detection of signals in random noise. Density operators take the
  • Rev. Lett. 72, 3439
  • 1994
  • Rev. A 47, 5138
  • 1993
  • Rev. D 23, 357
  • 1981
  • Rev. A 65, 033613
  • 2002
Quantum Detection and Estimation Theory (Academic Press
  • New York, 1976), Chap. VIII; A. S. Holevo, Probabilistic and Statistical Aspect of Quantum Theory
  • 1982
  • Rev. Lett. 77, 1413 (1996); R.F. Werner, Phys. Rev. A 40, 4277
  • 1989
  • Rev. A 64, 052106
  • 2001