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The notion of entangled states is very neat, it simply means non-separability of the states. Another important class of states that one often hears is the non-local state. But when do we say that a state $\rho$ is nonlocal?

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    $\begingroup$ Can you give references? I don't think terminology here (i.e. "nonlocal state") is entirely standardized. $\endgroup$ Jan 8, 2022 at 15:29

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The term "non-local states" most likely refers to states which allow to violate a Bell inequality. They give rise to statistics that cannot be explained with a local hidden variable model.

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