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Equation 23 · Part 7 · The Bit Comes Back Before the Bearing

Symbol epsilon

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\,\}.
ϵ\epsilon

What this part means

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

Its job in the formula

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

The passage around this formula

…quantum operations an agent holding both the full early radiation R and a further batch of radiation CtC_t collected up to time t can actually perform, whose entanglement 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…

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