One-shot holography

Understand

Following the work of [2008.03319], we define a generally covariant max-entanglement wedge of a boundary region $B$, which we conjecture to be the bulk region reconstructible from $B$.

• We similarly define a covariant min-entanglement wedge, which we conjecture to be the bulk region that can influence the state on $B$.
• We prove that the min- and max-entanglement wedges obey various properties necessary for this conjecture, such as nesting, inclusion of the causal wedge, and a reduction to the usual quantum extremal surface prescription in the appropriate special cases.
• These proofs rely on one-shot versions of the (restricted) quantum focusing conjecture (QFC) that we conjecture to hold.