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Equation 2 · Part 7 · How Fast Can a Horizon Learn Which Path You Took?

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∣Ψ(T)⟩=∣0⟩∣h0(T)⟩+∣1⟩∣h1(T)⟩2.|\Psi(T)\rangle= \frac{|0\rangle|h_0(T)\rangle+ |1\rangle|h_1(T)\rangle}{\sqrt 2}.
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What this part means

Take a square root.

Its job in the formula

Take a square root.

The passage around this formula

The labels zero and one denote paths, not energy eigenstates. After the system’s long-range field interacts with the inaccessible degrees of freedom, an idealized final pure state has the form ∣Ψ(T)⟩=∣0⟩∣h0(T)⟩+∣1⟩∣h1(T)⟩2|\Psi(T)\rangle= \frac{|0\rangle|h_0(T)\rangle+ |1\rangle|h_1(T)\rangle}{\sqrt 2}. Tracing out the field multiplies the off-diagonal element of the path density matrix by the conditional-state overlap

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Sources cited in the article section

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