separable density matrix product states
A density matrix ρ is called separable if it can be written as a convex sum of product states, namely





ρ
=

∑

j



p

j



ρ

j


(
A
)


⊗

ρ

j


(
B
)





{\displaystyle {\rho =\sum _{j}p_{j}\rho _{j}^{(A)}\otimes \rho _{j}^{(B)}}}


with 



0
≤

p

j


≤
1


{\displaystyle 0\leq p_{j}\leq 1}

 probabilities. By definition, a state is entangled if it is not separable.
