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∣ Ψ ⟩ = 1 5 ∣ ↑ ↑ ⟩ + 2 5 ∣ ↓ ↑ ⟩ − 2 5 ∣ ↓ ↓ ⟩ |\Psi\rangle = \frac{1}{\sqrt{5}}|\uparrow\uparrow\rangle +\frac{\sqrt{2}}{\sqrt{5}} |\downarrow\uparrow\rangle - \frac{\sqrt{2}}{\sqrt{5}} |\downarrow\downarrow\rangle ∣Ψ⟩=5 1∣↑↑⟩+5 2 ∣↓↑⟩−5 2 ∣↓↓⟩
Is the state ∣ Ψ ⟩ |\Psi\rangle ∣Ψ⟩above entangled?
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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byMatt DeCross