The entropy of entanglement is an entanglement measure for many-body quantum state.
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Bipartite entanglement entropy
Bipartite entanglement entropy is defined with respect to a bipartition of a state into two partitions
Von Neumann entanglement entropy
The bipartite Von Neumann entanglement entropy
where
Many entanglement measures reduce to the entropy of entanglement when evaluated on pure states. Among those are:
Some entanglement measures that do not reduce to the entropy of entanglement are:
Renyi entanglement entropies
The Renyi entanglement entropies
Note that the limit
Area law of bipartite entanglement entropy
A quantum state satisfies an area law if the leading term of the entanglement entropy grows at most proportionally with the boundary between the two partitions. Area laws are remarkably common for ground states of quantum many-body systems. This has important applications, one such application being that it greatly reduces the complexity of quantum many-body systems. The density matrix renormalization group and matrix product states, for example, implicitly rely on such area laws.