In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermal field double state. This identification has many puzzles, including the boundary descriptions of the event horizons, the interiors of the black hole, and the singularities. Compounding these mysteries is the fact that, while there is no interaction between the CFTs, observers from them can fall into the black hole and interact. We address these issues in this paper. In particular, we (i) present a boundary formulation of a class of in-falling bulk observers; (ii) present an argument that a sharp bulk event horizon can only emerge in the infinite N limit of the boundary theory; (iii) give an explicit construction in the boundary theory of an evolution operator for a bulk in-falling observer, making manifest the boundary emergence of the black hole horizons, the interiors, and the associated causal structure. A by-product is a concept called causal connectability, which is a criterion for any two quantum systems (which do not need to have a known gravity dual) to have an emergent sharp horizon structure.
In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermal field double state. In this paper we provide explicit constructions in the boundary theory of infalling time evolutions which can take bulk observers behind the horizon.The constructions also help to illuminate the boundary emergence of the black hole horizons, the interiors, and the associated causal structure. A key element is the emergence, in the large N limit of the boundary theory, of a type III 1 von Neumann algebraic structure from the type I boundary operator algebra and the half-sided modular translation structure associated with it.
For a multipart quantum system, a locally maximally entangled (LME) state is one where each elementary subsystem is maximally entangled with its complement. This paper is a sequel to [BRV], which gives necessary and sufficient conditions for a system to admit LME states in terms of its subsystem dimensions (d 1 , d 2 , . . . , d n ), and computes the dimension of the space S LM E /K of LME states up to local unitary transformations for all non-empty cases. Here we provide a pedagogical overview and physical interpretation of the underlying mathematics that leads to these results and give a large class of explicit constructions for LME states. In particular, we construct all LME states for tripartite systems with subsystem dimensions (2, A, B) and give a general representation-theoretic construction for a special class of stabilizer LME states. The latter construction provides a common framework for many known LME states. Our results have direct implications for the problem of characterizing SLOCC equivalence classes of quantum states, since points in S LM E /K correspond to natural families of SLOCC classes. Finally, we give the dimension of the stabilizer subgroup S ⊂ SL(d 1 , C) × · · · × SL(d n , C) for a generic state in an arbitrary multipart system and identify all cases where this stabilizer is trivial. sam.leutheusser@alumni.ubc.ca, jbryan@math.ubc.ca, reichst@math.ubc.ca, mav@phas.ubc.ca
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