Symbol S_m,n
,n is part of the quantity the equation computes from the expression on the right.
Read this term in its guide →Published equation contexts
Why this formula appears here
Hayden and Preskill’s own result, sharpened into an explicit, efficient decoding circuit by Yoshida and Kitaev, is that once scrambling of this kind has run for about , collecting only a handful more qubits of radiation than were thrown in — not a number that grows with the hole’s size — suppresses exponentially in that small handful [ 15 ] . The mechanism behind that exponential suppression is worth seeing exactly rather than taking on faith, and Page’s own formula for the average entanglement entropy of a subsystem of a random pure state supplies it. For an m -dimensional subsystem embedded in an mn -dimensional Haar-random pure state, . is exact [ 4 ] .…
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Symbol k
k appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol n
n occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Symbol m
m occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Read this term in its guide →Starting index or lower bound: k=n+1
This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.
Read this term in its guide →Ending index or upper bound: mn
This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.
Read this term in its guide →Denominator: 2n
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 73 · Evolutionary Physics
The Bit Comes Back Before the Bearing
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
Hayden and Preskill’s own result, sharpened into an explicit, efficient decoding circuit by Yoshida and Kitaev, is that once scrambling of this kind has run for about , collecting only a handful more qubits of radiation than were thrown in — not a number that grows with the hole’s size — suppresses exponentially in that small handful [ 15 ] . The mechanism behind that exponential suppression is worth seeing exactly rather than taking on faith, and Page’s own formula for the average entanglement entropy of a subsystem of a random pure state supplies it. For an m -dimensional subsystem embedded in an mn -dimensional Haar-random pure state, . is exact [ 4 ] .…
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