The Capability of Entanglement and Holographic Entropies at Finite Sources

arXiv:2608.26377v1 Announce Kind: cross
Summary: The Ryu-Takayanagi components equates the realm of a minimal floor with the von Neumann entropy of a boundary subregion, and leaves two issues about that identification open.
The primary is how sharply a geometry fixes an entropy. Fannes-Audenaert solutions with a Hilbert-space dimension, which diverges because the cutoff is eliminated nevertheless shut the 2 states are. We substitute it with the capability of entanglement, the variance of the modular power, whose sq. root grows just like the sq. root of the entangling space the place the dimensional issue grows just like the regulated quantity. The certain is dimension-free and saturated, and it makes the paradox of the entropy subextensive for any perturbation whose capability is small in contrast with $S_{vN}^2$ occasions the hint norm.
The second is what the realm means for a single state, since compression and dilution charges are outlined solely for a lot of copies whereas a geometry describes one. When a single reproduction saddle dominates close to $alpha = 1$, each clean R'{e}nyi entropy at fastened $alpha > 1$ agrees with $S_{vN}$ to $textit{O}(sqrt{S_{vN}})$, as do the sleek min- and max-entropies. The minimal floor due to this fact fixes each one-shot entropy of the state directly, with massive central cost taking part in the position of enormous copy quantity within the asymptotic equipartition property.
As a consequence we certain how far exterior the holographic entropy cone a holographic state can seem to fall, leaving estimation and certification open.



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