For a bipartite mixed state obtained by tracing out one subsystem of a tripartite Haar-random pure state, the relative entropy of entanglement equals log(d_A d_B / max(d_A,d_B,d_C)) plus an absolute constant, with high probability.
The relative entropy of entanglement of Schmidt correlated states and distillation
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abstract
We show that a mixed state $\rho=\sum_{mn}a_{mn}|m> < n|$ can be realized by an ensemble of pure states $\{p_{k}, |\phi_{k} > \}$ where $|\phi_{k}>=\sum_{m}\sqrt{a_{mm}}e^{i\theta_{m}^{k}}|m>$. Employing this form, we discuss the relative entropy of entanglement of Schmidt correlated states. Also, we calculate the distillable entanglement of a class of mixed states.
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Relative entropy of entanglement of Haar random states
For a bipartite mixed state obtained by tracing out one subsystem of a tripartite Haar-random pure state, the relative entropy of entanglement equals log(d_A d_B / max(d_A,d_B,d_C)) plus an absolute constant, with high probability.