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Equation 8 · Part 1 · How Fast Can a Horizon Learn Which Path You Took?

Symbol D

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.
DD

What this part means

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

Its job in the formula

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

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 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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