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Entanglement of qubits

  1. Dec 1, 2014 #1
    1. The problem statement, all variables and given/known data

    Determine which qubits are entangled:

    ##|\psi\rangle=\frac{1}{2}(|000\rangle+i|010\rangle+i|101\rangle-|111\rangle)##

    2. Relevant equations


    3. The attempt at a solution

    My idea was to first calculate the density operator
    ##\rho = |\psi\rangle \langle\psi|##
    and then find the partial trace over the second and the third qubit. Then from Schmidt rank I would know whether the first qubit is entangled with the rest of the system. Then I could repeat the procedure for the other qubits. However the result seams to be 0 and I don't even know how to interpret this result, nor how to find which of the three qubits are entangled.
     
  2. jcsd
  3. Dec 1, 2014 #2

    mfb

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    2016 Award

    Staff: Mentor

    Can you split the wavefunction into a product?
     
  4. Dec 2, 2014 #3
    Ok, I've tried separating one of the qubits from the rest to obtain a product state and succeded for the second one (B):
    ##|\psi\rangle = \frac{1}{2}(|0\rangle_B + i|1\rangle_B)(|00\rangle_{AC} + i|11\rangle_{AC})##,
    so it seams that qubit A is entangled with C (the first and the third).

    However I'm still left with a question why the method with the partial trace gave me 0. I would expect it to give the same result.
     
  5. Dec 2, 2014 #4

    mfb

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    Staff: Mentor

    I agree.

    Concerning the other method: Can you show your calculations?
     
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