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Maximal Quantum Fisher Information in a Mach-Zehnder Interferometer without initial parity

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 Added by Jing Liu
 Publication date 2014
  fields Physics
and research's language is English




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Mach-Zehnder interferometer is a common device in quantum phase estimation and the photon losses in it are an important issue for achieving a high phase accuracy. Here we thoroughly discuss the precision limit of the phase in the Mach-Zehnder interferometer with a coherent state and a superposition of coherent states as input states. By providing a general analytical expression of quantum Fisher information, the phase-matching condition and optimal initial parity are given. Especially, in the photon loss scenario, the sensitivity behaviors are analyzed and specific strategies are provided to restore the phase accuracies for symmetric and asymmetric losses.



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Possible paths of a photon passing through a nested Mach-Zehnder interferometer on its way to a detector are analyzed using the consistent histories formulation of quantum mechanics, and confirmed using a set of weak measurements (but not weak values). The results disagree with an analysis by Vaidman [ Phys. Rev. A 87 (2013) 052104 ], and agree with a conclusion reached by Li et al. [ Phys. Rev. A 88 (2013) 046102 ]. However, the analysis casts serious doubt on the claim of Salih et al. (whose authorship includes Li et al.) [ Phys. Rev. Lett. 110 (2013) 170502 ] to have constructed a protocol for counterfactual communication: a channel which can transmit information even though it contains a negligible number of photons.
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The Mach-Zehnder interferometric setup quantitatively characterizing the wave-particle duality implements in fact a joint measurement of two unsharp observables. We present a necessary and sufficient condition for such a pair of unsharp observables to be jointly measurable. The condition is shown to be equivalent to a duality inequality, which for the optimal strategy of extracting the which-path information is more stringent than the Jaeger-Shimony-Vaidman-Englert inequality.
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