← All parts of this equation

Equation 2 · Part 5 · How Fast Can a Horizon Learn Which Path You Took?

=

∣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}.
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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

Read this part in the article →

Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.