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Equation 2 · Part 1 · How Fast Can a Horizon Learn Which Path You Took?

Symbol Psi

∣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}.
Ψ\Psi

What this part means

Psi is part of the quantity the equation computes from the expression on the right.

Its job in the formula

Psi is part of the quantity the equation computes from the expression on the right.

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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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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