A bstract We study various notions of ‘subregion duality’ in the context AdS/CFT. highlight differences between ‘background wedge’ and ‘operator reconstruction wedges,’ providing a resolution to paradox raised [1]. Additionally, we elucidate distinctions four different wedges’ demonstrate how enhance proof for absence global symmetries geometrical states AdS/CFT [2, 3] as an example these distinctions.

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, 4 regions, we prove that strong subadditivity monogamy mutual information give complete set inequalities. This is in contrast to situation generic quantum systems, where not known or more regions. also find an infinite new family applicable 5 The all bounds phase space entropies, defining...

We present a general procedure for constructing tensor networks that accurately reproduce holographic states in conformal field theories (CFTs). Given state large-$N$ CFT with static, semiclassical gravitational dual, we build network by an iterative series of approximations eliminate redundant degrees freedom and minimize the bond dimensions resulting network. argue will match areas corresponding bulk surfaces. For 'tree' (i.e., those are constructed discretizing spacetime non-intersecting...

In this work we generalize the entanglement of purification and its conjectured holographic dual to conditional multipartite versions same, where optimization defining is now optimized in either a constrained way or over multiple parties. We separately derive new constraints on both object that match, further reinforcing likelihood conjecture. also show objects define, despite obeying several same inequalities, are not duals each other. Further, find inequalities true only for bulk objects,...

The multiscale entanglement renormalization ansatz (MERA) is a tensor network that provides an efficient way of variationally estimating the ground state critical quantum system. geometry resembles discretization spatial slices anti--de Sitter (AdS) spacetime and ``geodesics'' in MERA reproduce Ryu-Takayanagi formula for entropy boundary region terms bulk properties. It has therefore been suggested there could be AdS/MERA correspondence, relating states Hilbert space system to ones defined...

A bstract We study the conjectured holographic duality between entanglement of purification and wedge cross-section. generalize both quantities prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual tripartite information, as well a lower bound for information. are proven holographically general quantum states. In addition, we use cyclic entropy to derive new inequality cross-section, provide numerical evidence that corresponding may...

A bstract We propose a deterministic method to find all holographic entropy inequalities that have corresponding contraction maps and argue the completeness of our method. use triality between inequalities, partial cubes. More specifically, validity inequality is implied by existence map, which we prove be equivalent finding an isometric embedding contracted graph. Thus, virtue argued map proof method, problem maps, translate image graph give algorithmic solution this characterize complexity...

A bstract We discuss two methods that, through a combination of cyclically gluing copies given n -party boundary state in AdS/CFT and canonical purification, creates bulk geometry that contains homologous minimal surface with area equal to 2 or 4 times the entanglement wedge cross-section, depending on parity party number choice method. The areas surfaces are each dual entropies we define be candidates for reflected entropy. In context AdS 3 /CFT , provide interpretation our construction as...

We apply the support vector machine (SVM) algorithm to derive a set of entanglement witnesses (EW) identify patterns in families four-qubit states. The effectiveness SVM for practical EW implementations stems from coarse-grained description equivalent entangled quantum equivalence criteria our work is based on stochastic local operations and classical communication classification Werner numerically verify that approach provides an effective tool address witness problem when given family...

A bstract We establish an equivalence between non-isometry of quantum codes and state dependence operator reconstruction, discuss implications this for holographic duality. Specifically, we define quantitative measures describe bounds relating these quantities. In the context holography show that, assuming known gravitational path integral results overlaps semiclassical states, non-isometric bulk-to-boundary maps with a trivial kernel are approximately isometric bulk reconstruction...

A bstract We apply the bit thread formulation of holographic entanglement entropy to reduced states describing only geometry contained within an wedge. argue that a certain optimized configuration, which we construct, gives purification state full obeying precise set conditional mutual information relations. When this exists, establish, under assumptions, conjectured E P = W relation equating with area minimal cross section partitioning bulk Along way, comment on purifications states,...

We use the Holevo information to estimate distinguishability of microstates a black hole in anti-de Sitter space by measurements one can perform on subregion Cauchy surface dual conformal field theory. find that are not distinguishable at all until reaches certain size and perfect be achieved before covers entire surface. will compare our results with expectations from entanglement wedge reconstruction, tensor network models, bit threads interpretation Ryu-Takayanagi formula.

A bstract We posit a geometrical description of the entanglement purification for sub-regions in holographic CFT. The bulk naturally generalizes two-party case and leads to interesting inequalities among multi-party entanglements that can be geometrically proven from conjecture. Further, we study relationship between locally-AdS 3 spacetimes entropies multi-throated wormhole geometries constructed via quotienting by isometries. In particular, derive new are locally AdS relating subregions geometries.

In this work, we generalize the graph-theoretic techniques used for holographic entropy cone to study hypergraphs and their analogously-defined cone. This allows us develop a framework efficiently compute entropies prove inequalities satisfied by hypergraphs. doing so, discover class of quantum vectors which reach beyond those states obey constraints intimately related ones obeyed stabilizer linear ranks. We show that, at least up 4 parties, hypergraph is identical cone, thus demonstrating...

Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators Turing-complete computation. We discover quantum cellular (QCA) can exhibit complexity in the sense of science describes biology, sociology, and economics. QCA when evolving under "Goldilocks rules" we define by balancing activity stasis. Our Goldilocks rules generate robust dynamical features (entangled breathers), network structure dynamics consistent with...

Through the AdS/CFT correspondence, Lifshitz spacetimes describe field theories with dynamical scaling ($z \neq 1$). Although curvature invariants are small, metric exhibits a null singularity in IR large tidal force that excites string oscillator modes. However, is not vacuum solution of Einstein equations -- supported by nontrivial matter content which must be taken into account analyzing propagation test objects. In this paper, we consider interaction D0-brane density supports class...

We argue in a model-independent way that the Hilbert space of quantum gravity is locally finite-dimensional. In other words, density operator describing state corresponding to small region space, when such notion makes sense, defined on finite-dimensional factor larger space. Because potentially describes superpositions different geometries, it crucial we associate Hilbert-space factors with spatial regions only individual decohered branches universal wave function. discuss some implications...

We investigate the proposed connection between de Sitter spacetime and multiscale entanglement renormalization ansatz (MERA) tensor network, ask what can be learned via such a construction. show that quantum state obeys cosmic no-hair theorem: reduced density operator describing causal patch of MERA asymptotes to fixed point channel, just as spacetimes with positive cosmological constant asymptote space. The is potentially compatible weak form complementarity (local physics only describes...

We present a general procedure for constructing tensor networks geometric states in the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. Given state large-$N$ CFT with static, semiclassical gravitational dual, our produces network boundary whose internal geometry matches (a discretization of) bulk spacetime geometry. By invoking "holographic entanglement of purification" conjecture, construction can be made to capture structure at sub-AdS scales.

A quantum voting system is proposed in the tradition of game theory. It shown that this violates analogy Arrow's impossibility theorem, which makes claims about dictatorship a classical electoral system.

The Ryu–Takayanagi and Hubeny–Rangamani–Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of boundary theory. Using these formulae, we build on a result Alexakis, Balehowsky, Nachman to show in four dimensions, entropies regions disk topology uniquely fix metric any region foliated by corresponding HRT surfaces. More generally, for dimension , knowledge (variations the) areas two-dimensional boundary-anchored extremal surfaces fixes wherever reach. This...

A bstract We present a deterministic way of finding contraction maps for candidate holographic entanglement entropy inequalities modulo choices due to actual degeneracy. characterize its complexity and give an argument the completeness map proof method as necessary sufficient condition validity inequality entanglement.

We consider $AdS_2 \times R^2$ solutions supported by a magnetic field, such as those which arise in the near-horizon limit of magnetically charged $AdS_4$ Reissner-Nordstrom black branes. In presence an electrically scalar can be unstable to spontaneous formation vortex lattice. solve coupled partial differential equations govern scalar, gauge and metric degrees freedom lowest non-trivial order expansion around critical point, discuss corrections free energy thermodynamic functions arising...

We discuss the branching structure of quantum-gravitational wave function that describes evaporation a black hole. A global which initially classical Schwarzschild geometry is continually decohered into distinct semiclassical branches by emission Hawking radiation. The laws quantum mechanics dictate evolves unitarily, but this unitary evolution only manifest when considering description function; it not implemented time on single branch. Conversely, geometric notions like position or...

A bstract In the Hayden-Preskill thought experiment, Hawking radiation emitted before a quantum state is thrown into black hole used along with collected later for purpose of decoding state. natural question how recoverability affected if stored early damaged or subject to decoherence, and/or protocol imperfectly performed. We study in experiment presence decoherence noise storage radiation.