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Wave Mechanics in One Dimension — John S. Townsend
Physics — Quantum Mechanics · bell-states-sx-basis
Problem Show that the Bell basis state
∣ Φ ( + ) ⟩ = 1 2 ∣ + z , + z ⟩ + 1 2 ∣ − z , − z ⟩ |\Phi^{(+)}\rangle = \frac{1}{\sqrt{2}}|{+z}, {+z}\rangle + \frac{1}{\sqrt{2}}|{-z}, {-z}\rangle ∣ Φ ( + ) ⟩ = 2 1 ∣ + z , + z ⟩ + 2 1 ∣ − z , − z ⟩ S x S_x S x ∣ Φ ( + ) ⟩ = 1 2 ∣ + x , + x ⟩ + 1 2 ∣ − x , − x ⟩ |\Phi^{(+)}\rangle = \frac{1}{\sqrt{2}}|{+x}, {+x}\rangle + \frac{1}{\sqrt{2}}|{-x}, {-x}\rangle ∣ Φ ( + ) ⟩ = 2 1 ∣ + x , + x ⟩ + 2 1 ∣ − x , − x ⟩ ∣ Φ ( − ) ⟩ = 1 2 ∣ + z , + z ⟩ − 1 2 ∣ − z , − z ⟩ = 1 2 ∣ + x , − x ⟩ + 1 2 ∣ − x , + x ⟩ \begin{aligned}
|\Phi^{(-)}\rangle &= \frac{1}{\sqrt{2}}|{+z}, {+z}\rangle - \frac{1}{\sqrt{2}}|{-z}, {-z}\rangle \\
&= \frac{1}{\sqrt{2}}|{+x}, {-x}\rangle + \frac{1}{\sqrt{2}}|{-x}, {+x}\rangle
\end{aligned} ∣ Φ ( − ) ⟩ = 2 1 ∣ + z , + z ⟩ − 2 1 ∣ − z , − z ⟩ = 2 1 ∣ + x , − x ⟩ + 2 1 ∣ − x , + x ⟩ Browse the problem library