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How to calculate negativity measurement of quantum state?

  1. Aug 30, 2016 #1
    Good day,

    From my reading according to negativity for tripartite state, it is given as below;
    $$N_{ABC}(\rho)=(N_{A-BC}N_{B-AC}N_{C-AB})^{1/3}$$

    with

    $$N_{I-JK}=-2\Sigma_i\sigma_i(\rho^{TI})$$
    where
    $$\sigma_i(\rho^{TI})$$
    being the negative eigenvalues of
    $$\rho^{TI}$$,
    the partial transpose of $$
    \rho
    $$
    with respect to subsystem $$I$$.

    My problems:

    1.I not understand how it works. I find the eigenvalues but the value of eigenvalues is positive.But it mention the eigenvalues are negative. For example. I calculate GHZ state and the eigenvalues are positive. What its mean actually?

    2.It is same for $$
    N_{A-BC}
    $$ with another negativity formula given as below,
    $$
    N(\rho_A)=(Tr[\sigma_{A}^\dagger\sigma_{A}]^{1/2}-1)/2
    $$

    Please help me.

    Thank you
     
  2. jcsd
  3. Sep 4, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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