What is the Logarithmic Negativity of the Werner state

$$\rho_w = p|\Psi^-\rangle\langle\Psi^-|+\frac{1-p}{4}I_4$$

where $|\Psi^-\rangle = \frac{1}{\sqrt{2}}(|10\rangle-|01\rangle)$?

  • 3
    $\begingroup$ What did you try? $\endgroup$ Feb 10 at 23:44

Hint 1: Logarithmic negativity is easily computed once we know the eigenvalues of $\rho_w^\Gamma$ - where $^\Gamma$ denotes the partial transpose - since then it becomes a matter of substitution into the formulas in the Wikipedia article.

Hint 2: Finding the eigenvalues becomes easier once we observe that if $|v\rangle$ is an eigenvector of $\rho_w^\Gamma$ then $|v\rangle$ is an eigenvector of $(|\Psi^-\rangle\langle\Psi^-|)^\Gamma$.


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