= Separable quantum state
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= Separable state
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A bipartite <quantum state> is separable when its <density operator> is a <convex combination> $\sum_jp_j\rho_j^A\otimes\rho_j^B$ of product states; otherwise it has <entanglement>. Operationally, Alice and Bob can prepare a <separable quantum state> by sharing a classical random label $j$ and each preparing the corresponding local state.
Separable does not mean uncorrelated. The mixture in <Bell correlations versus a classical mixture> is separable with two terms of weight $1/2$, yet the parties' $Z$ records agree perfectly. A single product state would give independent local outcomes. Allowing a mixture of products captures shared classical randomness; excluding this possibility would incorrectly classify ordinary correlations as <entanglement>.
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