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How can I do when I make a Log2 towards zero?

  1. Aug 1, 2016 #1
    Good day,

    1. The problem statement, all variables and given/known data

    I want to make a measurement on qubit by using formula von Neumann entropy using Mathematica given as below;

    2. Relevant equations

    (ρ)=−Tr(ρlog2ρ)

    3. The attempt at a solution

    The
    ρ={{0.5,0},{0,0.5}}


    My problem is, when I make the

    log2{{0.5,0},{0,0.5}}
    I get the output

    {{−1,∞},{∞,−1}}

    How can I deal with this value in my measurement since it cannot be calculated?

    Thank you.
     
  2. jcsd
  3. Aug 1, 2016 #2

    mfb

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    Looks like you take the logarithm of each entry in the matrix. I don't think that is what you want.
    Matrix log?
     
  4. Aug 1, 2016 #3

    BvU

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    Can you put in some lower limit, like ##2^{-20} ## ?
    [edit] Ha ! o:)

    [edit2] Isn't it so that you have already diagonalized ##\rho## so you can use the ## S = - \sum \eta\ln\eta ## here ?
     
    Last edited: Aug 1, 2016
  5. Aug 1, 2016 #4

    I'm not sure about the matrix log.I think it different
     
  6. Aug 1, 2016 #5

    thank you for the input. I will search it and learn
     
  7. Aug 1, 2016 #6

    BvU

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    My guess is the matrix log coincides with taking log of the diagonal elements once the matrix is diagonalized ...
     
  8. Aug 1, 2016 #7

    it means only for diagonal matrices?
     
  9. Aug 1, 2016 #8

    BvU

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    Just a guess. :smile:
     
  10. Aug 1, 2016 #9
    ok. thank you very much. i will look about it.
     
  11. Aug 1, 2016 #10

    mfb

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    Sure. This should be easy to see if you take the matrix exponential again.
     
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