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Unsharp measurement

  1. Sep 21, 2014 #1

    naima

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    How can we see if a quantum measurement is sharp or unsharp ? can we measure unsharpness?
    Thanks
     
  2. jcsd
  3. Sep 21, 2014 #2

    atyy

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  4. Sep 21, 2014 #3

    naima

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    Could you look at this paper.
    www.johnboccio.com/research/quantum/notes/Operational_QM.pdf
    Busch gives a formal definition of unsharpness on page 36. I do not undestand what is the physics behind that. Could you comment.
    The author writes Eu (H) = Ep (H)\P(H)
    So unsharp measurements have outputs that are non projector effects.
    The question is now: How can i recognize a non projector?
     
    Last edited: Sep 21, 2014
  5. Sep 23, 2014 #4

    naima

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    I am beginning to see how it works.
    In operational quantum mechanics, the outcomes of an apparatus are no more associated to vectors in H but to operators on H.
    take an optical device with one input channel receiving linear polarized photons and with 3 output channels associated to
    \begin{pmatrix}
    cos^2(\alpha) & 0 \\
    0 & 0
    \end{pmatrix}
    \begin{pmatrix}
    sin^2(\alpha) & 0 \\
    0 & 0
    \end{pmatrix}
    \begin{pmatrix}
    0 & 0 \\
    0 & 1
    \end{pmatrix}
    They sum to Id
    There is a difference between the three outputs:
    If you prepare down photons and send them thru the device the third detector detector 1 and 2 will not click and the 3th will click. we have here a sharp detection.
    We cannot prepare a state so that the only first detector will click detectors 1 and 2 are associated to unsharp measurement (unless alpha 0)
    if ##\alpha = \pi /2## we have a maximal unsharpness for detectors 1 and 2.
    they will have a 1/2 probability to click for an up photon
     
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