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Equation 8 · Part 2 · How Fast Can a Horizon Learn Which Path You Took?

Symbol T

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.
TT

What this part means

T is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

T is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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 variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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