The density matrix renormalization group and matrix product states, for example, implicitly rely on such area laws. This has important applications, one such application being that it greatly reduces the complexity of quantum many-body systems. Īrea law of bipartite entanglement entropy Ī 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.Īrea laws are remarkably common for ground states of local gapped quantum many-body systems. A non-zero topological entanglement entropy reflects the presence of long range quantum entanglements in a many-body quantum state. More mathematically if a state describing two subsystems A and B | Ψ A B ⟩ = | ϕ A ⟩ | ϕ B ⟩. The topological entanglement entropy or topological entropy, usually denoted by, is a number characterizing many-body states that possess topological order. the subsystem is in a mixed state, it indicates the two subsystems are entangled. The entropy of entanglement (or entanglement entropy) is a measure of the degree of quantum entanglement between two subsystems constituting a two-part. The entropy of entanglement is the Von Neumann entropy of the reduced density matrix for any of the subsystems. Given a pure bipartite quantum state of the composite system, it is possible to obtain a reduced density matrix describing knowledge of the state of a subsystem. The entropy of entanglement (or entanglement entropy) is a measure of the degree of quantum entanglement between two subsystems constituting a two-part composite quantum system.
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