Negativity

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The logarithmic negativity is an entanglement monotone which, like the entanglement of formation, provides an upper bound on the distillable entanglement but is also computable for mixed states. The logarithmic negativity is defined as


E_N(\rho) \equiv \log_2 (2\mathcal{N}(\rho) +1 )

where \mathcal{N}(\rho) is the negativity of the state. The negativity is defined as the absolute sum of the negative eigenvalues of the partial transpose with respect to subsystem A, \rho^{T_A}. So


    \mathcal{N}(\rho) \equiv \sum_i
        \frac{|\lambda_{i}|-\lambda_{i}}{2}

where λi are all of the eigenvalues.