Qubits Entanglement: Calculate & Interpret

[amgo100]

Homework Statement

Determine which qubits are entangled:

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

Homework Equations

The Attempt at a Solution

[/B]
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.

 

[mfb]

Can you split the wavefunction into a product?

 

[amgo100]

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.

 

[mfb]

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).

I agree.

Concerning the other method: Can you show your calculations?