# How to calculate negativity measurement of quantum state?

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1. Aug 30, 2016

### munirah

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,
$$N(\rho_A)=(Tr[\sigma_{A}^\dagger\sigma_{A}]^{1/2}-1)/2$$

Thank you

2. Sep 4, 2016