- #1
Alex Dingo
- 6
- 1
Hi,
I'm currently working through a tensor product example for a two qubit system.
For the expression:
$$
\rho_A = \sum_{J=0}^{1}\langle J | \Psi \rangle \langle \Psi | J \rangle
$$
Which has been defined as from going to a global state to a local state.
Here
$$ |\Psi \rangle = |\Psi^+ \rangle = \frac{1}{\sqrt{2}}(|01\rangle + |10\rangle ) $$
I'm not sure how to get from here to here: $$
\rho_A = \frac{1}{2} |1\rangle\langle 1| + \frac{1}{2} |0\rangle\langle 0|
$$
I'm finding that the terms in the summation reduce to dot products rather than the form of the answer. i.e
$$
\rho_A = \frac{1}{2}(\langle 0 | 01 \rangle + \langle 0 | 10 \rangle + \langle 1| 01 \rangle + \langle 1 | 10 \rangle + \langle 01 | 0 \rangle + \langle 10 | 0 \rangle + \langle 10 | 1 \rangle + \langle 01 | 1 \rangle )
$$
Which is where I'm thinking of going wrong?
Thanks for any help.
I'm currently working through a tensor product example for a two qubit system.
For the expression:
$$
\rho_A = \sum_{J=0}^{1}\langle J | \Psi \rangle \langle \Psi | J \rangle
$$
Which has been defined as from going to a global state to a local state.
Here
$$ |\Psi \rangle = |\Psi^+ \rangle = \frac{1}{\sqrt{2}}(|01\rangle + |10\rangle ) $$
I'm not sure how to get from here to here: $$
\rho_A = \frac{1}{2} |1\rangle\langle 1| + \frac{1}{2} |0\rangle\langle 0|
$$
I'm finding that the terms in the summation reduce to dot products rather than the form of the answer. i.e
$$
\rho_A = \frac{1}{2}(\langle 0 | 01 \rangle + \langle 0 | 10 \rangle + \langle 1| 01 \rangle + \langle 1 | 10 \rangle + \langle 01 | 0 \rangle + \langle 10 | 0 \rangle + \langle 10 | 1 \rangle + \langle 01 | 1 \rangle )
$$
Which is where I'm thinking of going wrong?
Thanks for any help.