Forming the most general two qubit entangled state & parametrizing it.

[shakgoku]

I have seen four two qubit entangled states of the form:

$ \frac{1}{\sqrt{2}} \left | 00 \right > \pm \left | 11 \right >$

$ \frac{1}{\sqrt{2}} \left | 01 \right > \pm \left | 10 \right >$

I want to write a most general two qubit entangled state. I presume it can be of the form:

$ \alpha \left | 00 \right > + \beta \left | 11 \right > + \gamma \left | 01 \right > + \delta \left | 10 \right >$

where the $\alpha, \beta ...$ are complex numbers. If this is correct, How can I parametrize these constants using least number of free parameters?

 

[jk22]

the states are orthogonal and you get for the normalization condition alpha^2+beta^2+gamma^2 +delta^2=1
Hence alpha=sin x sin y sin z exp ia
Beta=sin x sin y cos z exp ib
Gamma=sin x cos y exp ic
Delta=cos x exp id
For example. I am not sure if its the most general form.