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 quantum state 
on a finite lattice domain
and a subset 
, put 
, where 
is the partial trace
over the complement of 
. Using natural logarithms,
the bound has the form
 |
where 
consists of nearest-neighbor edges crossing the cut
and 
is a constant independent of the region and lattice
size for the family under consideration. For a tensor
product of pure quantum states, the reduced
von Neumann entropy is zero (Eisert et al.
2010).
