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Differences between pure/mixed/entangled/separable/superposed states
If ψAB is an entangled i.e. not separable state, i.e. if it cannot be written as |ψA⟩⊗|ψB⟩ for any states |ψA⟩ and |ψB⟩, then the tracing over has the effect of picking all the terms in |ψAB⟩, forgetting about their dependence on the B degrees of freedom, and writing their probabilities on the diagonal of ρA.- Isn't that only true in the (Schmidt decomposition for ψAB) basis?