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Equation 8 · Part 3 · How Fast Can a Horizon Learn Which Path You Took?

Symbol h_0

D(T)=12∥∣h0⟩⟨h0∣−∣h1⟩⟨h1∣∥1.D(T)=\frac12 \left\| |h_0\rangle\langle h_0|- |h_1\rangle\langle h_1| \right\|_1.
h0h_0

What this part means

h0h_0 is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

h0h_0 is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

Assume for the moment that |h0h_0⟩\rangle and |h1h_1⟩\rangle are pure, normalized, and prepared with equal prior probability. Define their trace distinguishability D(T)=12∥∣h0⟩⟨h0∣−∣h1⟩⟨h1∣∥1D(T)=\frac12 \left\| |h_0\rangle\langle h_0|- |h_1\rangle\langle h_1| \right\|_1. For two pure states,

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Learn the underlying idea

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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