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Equation 23 · Part 1 · The Bit Comes Back Before the Bearing

Symbol epsilon_L

ϵL(t)  =  min⁡R[ 1−Fe(R∘Nt,  id) ],tL(ϵ)  =  min⁡{ t:ϵL(t)≤ϵ }.\epsilon_L(t) \;=\; \min_{\mathcal R}\Big[\,1 - F_e\big(\mathcal R \circ \mathcal N_t,\; \mathrm{id}\big)\,\Big], \qquad t_L(\epsilon) \;=\; \min\{\,t : \epsilon_L(t) \le \epsilon\,\}.
ϵL\epsilon_L

What this part means

a dimensionless number in [0,1] , and tLt_L has units of time.

Its job in the formula

epsilonLn_L is the quantity selected or evaluated by the optimization written on the right.

Where the article explains it

CtC_t induced by the hole’s own scrambling dynamics up to time t ; ϵL(t)\epsilon_L(t) is a dimensionless number in [0,1] , and tLt_L has units of time.

The passage around this formula

…fidelity to the identity channel on A is within ϵ\epsilon of perfect, ϵL(t)  =  min⁡R[ 1−Fe(R∘Nt,  id) ],tL(ϵ)  =  min⁡{ t:ϵL(t)≤ϵ }\epsilon_L(t) \;=\; \min_{\mathcal R}\Big[\,1 - F_e\big(\mathcal R \circ \mathcal N_t,\; \mathrm{id}\big)\,\Big], \qquad t_L(\epsilon) \;=\; \min\{\,t : \epsilon_L(t) \le \epsilon\,\}. Nt\mathcal N_t is the effective channel from A to R\!∪\cup\!CtC_t induced by the hole’s own scrambling dynamics up to time t ; ϵL(t)\epsilon_L(t) is a dimensionless number in [0,1] , and tLt_L has units of time. This is a yes-or-no-shaped promise sharpened into a number: either a decoder within ϵ\epsilon of perfect exists on the stated resources, or it does not, and ϵL(t)\epsilon_L(t) falls, in the regime this article works in, toward…

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Learn the underlying idea

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 article section

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