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Entanglement Area Law


An entanglement area law is a bound on the von Neumann entropy of a reduced quantum state by the size of the boundary separating a region from its complement. For a pure state Omega on a lattice domain Lambda, put rho_A=Tr_(Lambda\A)|Omega><Omega|. Using natural logarithms, the bound has the form

 -Tr(rho_Alnrho_A)<=C|partial_LambdaA|,

where partial_LambdaA consists of nearest-neighbor edges crossing the cut. For a product state the entropy is zero.


See also

Ground State, Partial Trace, Projected Entangled-Pair State, Spectral Gap, von Neumann Entropy

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References

Eisert, J.; Cramer, M.; and Plenio, M. B. "Colloquium: Area Laws for the Entanglement Entropy." Rev. Mod. Phys. 82, 277-306, 2010. https://doi.org/10.1103/RevModPhys.82.277.

Cite this as:

Weisstein, Eric W. "Entanglement Area Law." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EntanglementAreaLaw.html

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