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Quantum information (sum is 4 or 6)

  1. Oct 13, 2007 #1
    1. The problem statement, all variables and given/known data
    We have two people, Alice and Bob. They get numbers random, but we have two cases.
    Firs case: [tex]\sum6[/tex]
    If:
    Bob get 6 then Alice get 0
    Bob get 5 then Alice get 1
    Bob get 4 then Alice get 2
    Bob get 3 then Alice get 3
    Bob get 2 then Alice get 4

    Second case [tex]\sum4[/tex]
    If
    Bob get 4 then Alice get 0
    Bob get 3 then Alice get 1
    Bob get 2 then Alice get 2
    Bob get 1 then Alice get 3
    Bob get 0 then Alice get 4

    They don't know, what number do have by other and they can communicate nobody. They can use whatever gate (e.g. Hadamard, CNOT, fCNOT). Alice and Bob can just 1-1 bit sending out. A judge get these bits and he can decide, how it is a first case [tex]\left(\sum6\right)[/tex] or a second case[tex]\left(\sum4\right)[/tex] . Also we need just know, the sum was 4 or 6.
    Both can use any Bell state.
    I append a drawing, how it is looking out.


    2. Relevant equations
    Bell states
    [tex]\left|\beta_{00}\right\rangle= \frac{1}{\sqrt{2}}\left(\left|0\right\rangle\ \left|0\right\rangle\ +\left|1\right\rangle\ \left|1\right\rangle\ \right)[/tex]
    [tex]\left|\beta_{01}\right\rangle= \frac{1}{\sqrt{2}}\left(\left|0\right\rangle\ \left|1\right\rangle\ +\left|1\right\rangle\ \left|0\right\rangle\ \right)[/tex]
    [tex]\left|\beta_{10}\right\rangle= \frac{1}{\sqrt{2}}\left(\left|0\right\rangle\ \left|0\right\rangle\ -\left|1\right\rangle\ \left|1\right\rangle\ \right)[/tex]
    [tex]\left|\beta_{11}\right\rangle= \frac{1}{\sqrt{2}}\left(\left|0\right\rangle\ \left|1\right\rangle\ -\left|1\right\rangle\ \left|0\right\rangle\ \right)[/tex]


    3. The attempt at a solution
    I would like to know, how can I make this problem or what name can I find this solution.
     

    Attached Files:

  2. jcsd
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