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Quantum Fourier Transform of Periodic States

  1. Oct 17, 2011 #1

    This is probably trivial, but I don't see it and would therefore appreciate receving inputs.

    Suppose we define a state

    [tex]|\phi_{lr}\rangle = \sum_{n=0}^{N/r - 1}\sqrt{\frac{r}{N}}|l + n r\rangle[/tex]

    How is the quantum Fourier transform of this state equal to

    [tex]|\tilde{\phi}_{lr}\rangle = \sum_{m=0}^{r-1}\alpha_{m}\left|\frac{m N}{r}\right\rangle[/tex]

    where [itex]|\alpha| = \sqrt{1/r}[/itex] for all [itex]m[/itex]?

    This is from http://www-bcf.usc.edu/~tbrun/Course/lecture13.pdf.

    Thanks in advance!
  2. jcsd
  3. Apr 10, 2012 #2
    I have the same question on it... Any help?
  4. Apr 10, 2012 #3
    you must use the Poisson summation formula.
  5. Apr 10, 2012 #4
    I have just proved it using similar formulas. Thanks!
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