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Homework Help: Applying a gate to entangle states

  1. Apr 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Part of a past paper, I can do all of the question a-d without problems but the second part of e) is giving me trouble.

    So you have the following state

    [itex]\frac{1}{\sqrt{2}}[/itex]([itex]\mid 0 \rangle[/itex][itex]_{A}[/itex] + [itex]\mid 1 \rangle[/itex][itex]_{A}[/itex])[itex]\mid 0 \rangle[/itex][itex]_{B}[/itex][itex]\mid 0 \rangle[/itex][itex]_{C}[/itex]

    You apply a three bit parity gate, which you do in previous parts, the table looks as follows

    000 [itex]\rightarrow[/itex] 000
    001 [itex]\rightarrow[/itex] 001
    010 [itex]\rightarrow[/itex] 011
    011 [itex]\rightarrow[/itex] 010
    100 [itex]\rightarrow[/itex] 101
    101 [itex]\rightarrow[/itex] 100
    110 [itex]\rightarrow[/itex] 110
    111 [itex]\rightarrow[/itex] 111

    Which gives you

    [itex]\frac{1}{\sqrt{2}}[/itex]([itex]\mid 0 \rangle[/itex][itex]_{A}[/itex][itex]\mid 0 \rangle[/itex][itex]_{C}[/itex] + [itex]\mid 1 \rangle[/itex][itex]_{A}[/itex][itex]\mid 1 \rangle[/itex][itex]_{C}[/itex])[itex]\mid 0 \rangle[/itex][itex]_{B}[/itex]

    So A and C are entangled.

    The question then asks you to chose a new initial state so that after applying G and taking a measurement of C, A & B are entangled.

    2. Relevant equations


    3. The attempt at a solution

    I'm not entirely sure what to do, the gate only affects C, taking a measurement of C suggests that C should be in a superposition? Pretty confused on this one, but it is the last part of a question so it's supposed to be more a head-scratcher rather than bookwork.
  2. jcsd
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