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Equation 77 · Part 1 · The Bit Comes Back Before the Bearing

Symbol S_2,16

⟨S2,16⟩=0.6465\langle S_{2,16}\rangle = 0.6465
S2,16S_{2,16}

What this part means

S2S_2,16 is part of the quantity the equation computes from the expression on the right.

Its job in the formula

S2S_2,16 is part of the quantity the equation computes from the expression on the right.

The passage around this formula

is exact [ 4 ] . Fixing m=2 (a single qubit) and letting n — the effective size of everything else the qubit could be entangled with — grow gives ⟨\langle S2,4S_{2,4}⟩\rangle = 0.5095 nats, ⟨\langle S2,16S_{2,16}⟩\rangle = 0.6465 nats, and ⟨\langle S2,64S_{2,64}⟩\rangle = 0.6814 nats, closing in on the ceiling ln⁡\ln 2 = 0.6931 nats. The residual gap to that ceiling shrinks by a factor of 3.94 when n quadruples from 4 to 16 , and by 3.98 when it quadruples again from 16 to 64 — converging, as more radiation-sized dimension is added two qubits at a time, on a clean factor of four per doubling of collected qubits, or two per single qubit. This is an exact, hand-computable corroboration of the folklore “each extra…

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