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

  1. Apr 23, 2013 #1
    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?
  2. jcsd
  3. Apr 23, 2013 #2
    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. Im not sure if its the most general form.
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