RDM notation equation help

[Nusc]

Homework Statement

$$\hat{\rho} = \left|\Phi_{AB}\right\rangle\left\langle\Phi{AB}\right| = \alpha ( |Z+>_A|Z+>_B+|X+>_A|X+>_B)* \alpha ( <Z+|_B <Z+|_A+<X+|_B<X+|_A)$$

Is |Z+>_A|Z+>_B similar to |00> ? I'm confused wiht notation

Homework Equations

The Attempt at a Solution

 

[Fredrik]

I think you will have to explain what |00> is, and what you mean by "similar". Also, what does |X+> mean? An eigenstate of the x-component of spin?

 

[Nusc]

Ignore the question on |00>.

Yes.

 

[Fredrik]

That was the only question you asked.

 

[Nusc]

referring to the other post: https://www.physicsforums.com/showthread.php?t=389293

Once I have found the reduxed density matrix

p_a with a basis of {
| 1 |
| 0 | }

and p_b with a basis of{

| -1/4(sqrt2) |
| 1 | }


how do I finish off the problem to find the decomposition?