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Equation 2 · Part 4 · How Fast Can a Horizon Learn Which Path You Took?

Symbol h_1

∣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}.
h1h_1

What this part means

h1h_1 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

h1h_1 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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