- #1
munirah
- 31
- 0
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
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