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∣f⟩=12(∣↑⟩+i∣↓⟩)|f\rangle = \tfrac{1}{\sqrt2}(|{\uparrow}\rangle+i|{\downarrow}\rangle)

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​ 1 ​ ( ∣ ↑ ⟩ + ∣ ↓ ⟩) , and postselect along y , |f⟩\rangle = 12(∣↑⟩+i∣↓⟩)\tfrac{1}{\sqrt2}(|{\uparrow}\rangle+i|{\downarrow}\rangle) . Then ⟨\langle f|ψ\psi⟩\rangle = 12(1−i)\tfrac12(1-i) and ⟨\langle f|σz\sigma_z|ψ\psi⟩\rangle = 12(1+i)\tfrac12(1+i) , so the weak value of σz\sigma_z is

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∣f⟩=12(∣↑⟩+i∣↓⟩)|f\rangle = \tfrac{1}{\sqrt2}(|{\uparrow}\rangle+i|{\downarrow}\rangle)

Equation 96 · Evolutionary Physics

The Atlas That Refuses to Close

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

​ 1 ​ ( ∣ ↑ ⟩ + ∣ ↓ ⟩) , and postselect along y , |f⟩\rangle = 12(∣↑⟩+i∣↓⟩)\tfrac{1}{\sqrt2}(|{\uparrow}\rangle+i|{\downarrow}\rangle) . Then ⟨\langle f|ψ\psi⟩\rangle = 12(1−i)\tfrac12(1-i) and ⟨\langle f|σz\sigma_z|ψ\psi⟩\rangle = 12(1+i)\tfrac12(1+i) , so the weak value of σz\sigma_z is

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