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Is the following state ∣Ψ⟩|\Psi\rangle∣Ψ⟩ entangled?
∣Ψ⟩=12(∣↓↓⟩+∣↓↑⟩).|\Psi\rangle = \frac{1}{\sqrt{2}} (|\downarrow\downarrow\rangle + |\downarrow\uparrow\rangle).∣Ψ⟩=21(∣↓↓⟩+∣↓↑⟩).
Note: The notation ∣↑↓⟩=∣↑⟩⊗∣↓⟩|\uparrow\downarrow\rangle = |\uparrow\rangle \otimes |\downarrow\rangle∣↑↓⟩=∣↑⟩⊗∣↓⟩ is a common shorthand for tensor products of spin states.
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