arXiv subjects
Publications and source records attributed to Sirui Shuai.
We show that every holographic entropy inequality can be recast in the form: "some entanglement wedges reach deeper in the bulk than some other entanglement wedges." When the inequality is saturated, the two sets of wedges reach equally deep. Because bulk depth geometrizes CFT scales, the inequalities enforce and protect the holographic Renormalization Group.
We interpret holographic entropy inequalities in terms of erasure correction. The non-saturation of an inequality is a necessary condition for certain schemes of holographic erasure correction, manifested in the bulk as non-empty overlaps of corresponding entanglement wedges.
The default way of proving holographic entropy inequalities is the contraction method. It divides Ryu-Takayanagi (RT) surfaces on the `greater than' side of the inequality into segments, then glues the segments into candidate RT surfaces for terms on the `less than' side. Here we discuss how proofs by contraction are constrained and informed by entanglement wedge nesting (EWN) -- the property that enlarging a boundary region can only enlarge its entanglement wedge. We propose that: (i) all proofs by contraction necessarily involve candidate RT surfaces, which violate EWN; (ii) violations of EWN in contraction proofs of maximally tight inequalities occur commonly and -- where this can be quantified -- with maximal density near boundary conditions; (iii) the non-uniqueness of proofs by contraction reflects inequivalent ways of violating EWN. As evidence and illustration, we study the recently discovered infinite families of holographic entropy inequalities, which are associated with tessellations of the torus and the projective plane. We explain the logic, which underlies their proofs by contraction. We find that all salient aspects of the requisite contraction maps are dictated by EWN while all their variable aspects set the scheme for how to violate EWN. We comment on whether the tension between EWN and contraction maps might help in characterizing maximally tight holographic entropy inequalities.
We revisit information retrieval from evaporating black holes in the Hayden-Preskill protocol, treating the black hole dynamics as Haar-random. We compute, down to the first exponentially suppressed terms, all integer-indexed Rényi mutual informations between a black hole, its radiation, and a reference that catalogues Alice's diaries. We find that dropping a diary into a young black hole effectively delays the Page time. We also compute the radiation : diary reflected Rényi entropies, and identify a technical reason why they cannot be continued to the reflected entropy by the replica trick.
We prove two new infinite families of holographic entropy inequalities. A key tool is a graphical arrangement of terms of inequalities, which is based on entanglement wedge nesting (EWN). It associates the inequalities with tessellations of the torus and the projective plane, which reflect a certain topological aspect of EWN. The inequalities prove a prior conjecture about the structure of the holographic entropy cone and show an interesting interplay with differential entropy.
The holographic entropy cone identifies entanglement entropies of field theory regions, which are consistent with representing semiclassical spacetimes under gauge/gravity duality; it is currently known up to 5 regions. We point out that average entropies of p-partite subsystems can be similarly analyzed for arbitrarily many regions. We conjecture that the holographic cone of average entropies is simplicial and specify all its bounding inequalities. Its extreme rays combine features of bipartite and perfect tensor entanglement, and correspond to stages of unitary evaporation of old black holes.