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Equation 13 · Part 3 · How Fast Can a Horizon Learn Which Path You Took?

Symbol h_2

χH(T)=h2 ⁣(1+V(T)2).\chi_H(T)= h_2\!\left(\frac{1+V(T)}{2}\right).
h2h_2

What this part means

h2h_2 is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

h2h_2 is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

There is another number in the same pair of states. The Holevo quantity of the equal-prior pure ensemble is χH(T)=h2 ⁣(1+V(T)2)\chi_H(T)= h_2\!\left(\frac{1+V(T)}{2}\right). It is the von Neumann entropy of the average conditional state because each conditional state is pure. Holevo’s theorem makes this quantity an upper bound on classical information accessible through a quantum measurement, not a guarantee that an arbitrary one-copy receiver attains it [ 13 ] . Fuchs and Caves developed ensemble-dependent bounds that make the gap between a state’s information content and a receiver’s accessible information explicit [ 15 ] .

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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 surrounding passage

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