## Applying a gate to entangle states

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

$\frac{1}{\sqrt{2}}$($\mid 0 \rangle$$_{A}$ + $\mid 1 \rangle$$_{A}$)$\mid 0 \rangle$$_{B}$$\mid 0 \rangle$$_{C}$

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

000 $\rightarrow$ 000
001 $\rightarrow$ 001
010 $\rightarrow$ 011
011 $\rightarrow$ 010
100 $\rightarrow$ 101
101 $\rightarrow$ 100
110 $\rightarrow$ 110
111 $\rightarrow$ 111

Which gives you

$\frac{1}{\sqrt{2}}$($\mid 0 \rangle$$_{A}$$\mid 0 \rangle$$_{C}$ + $\mid 1 \rangle$$_{A}$$\mid 1 \rangle$$_{C}$)$\mid 0 \rangle$$_{B}$

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

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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.
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 Tags gate, parity gate, quantum, quantum computing

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