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.
Entanglement and local information access for graph states
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abstract
We exactly evaluate a number of multipartite entanglement measures for a class of graph states, including d-dimensional cluster states (d = 1,2,3), the Greenberger-Horne-Zeilinger states, and some related mixed states. The entanglement measures that we consider are continuous, `distance from separable states' measures, including the relative entropy, the so-called geometric measure, and robustness of entanglement. We also show that for our class of graph states these entanglement values give an operational interpretation as the maximal number of graph states distinguishable by local operations and classical communication (LOCC), as well as supplying a tight bound on the fixed letter classical capacity under LOCC decoding.
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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.