We embed relativistic quantum information protocols in AdS/CFT: an Unruh-DeWitt detector coupled to a local primary of a holographic CFT has a reduced state fixed by the universal boundary Wightman function. We find that the mana generated in a qutrit probe reads off the boundary condition of the dual bulk scalar, de-excitation spectroscopy tracks the double-trace flow through the lowest cylinder gap, and a local boundary detector is inequivalent to the HKLL representation of a bulk-local one.
Comments
v1: 7 pages. Comments are welcome. v2: "double-trace flow" and "local versus HKLL-smeared detector protocols" added
We embed relativistic quantum information protocols in AdS/CFT: an Unruh-DeWitt detector coupled to a local primary of a holographic CFT has a reduced state fixed by the universal boundary Wightman function. We find that the mana generated in a qutrit probe reads off the boundary condition of the dual bulk scalar, de-excitation spectroscopy tracks the double-trace flow through the lowest cylinder gap, and a local boundary detector is inequivalent to the HKLL representation of a bulk-local one.
The AdS/CFT correspondence conjectures a duality between quantum gravity theories in anti-de Sitter (AdS) spacetime and conformal field theories (CFTs) on the boundary. One intriguing aspect of this correspondence is that it offers a pathway to explore quantum gravity through tabletop experiments. Recently, a multi-scale entanglement renormalization ansatz (MERA) model of AdS/CFT that can be implemented using contemporary quantum simulators has been proposed [R. Sahay, M. D. Lukin, and J. Cotler, arXiv:2401.13595 (2024)]. Particularly, local bulk excitations (entitled "hologrons") manifesting attractive interactions given by AdS gravity were found. However, the fundamental question concerning the stability of these identified hologrons is still left open. Here, we address this question and find that hologrons are unstable during dynamic evolution. In searching for stable bulk excitations with attractive interactions, we find they can be constructed by the local primary operators in the boundary CFT. Furthermore, we identify a class of boundary excitations that exhibit the bizarre behavior of "holographic transportation", which can be directly observed on the boundary system implemented in experiments.
We further develop perturbative methods used to calculate entanglement entropy (EE) away from an interacting CFT fixed point. At second order we find certain universal terms in the renormalized EE which were predicted previously from holography and which we find hold universally for relevant deformations of any CFT in any dimension. We use both replica methods and direct methods to calculate the EE and in both cases find a non-local integral expression involving the CFT two point function. We show that this integral expression can be written as a local integral over a higher dimensional bulk modular hamiltonian in an emergent AdS space-time. This bulk modular hamiltonian is associated to an emergent scalar field dual to the deforming operator. We generalize to arbitrary spatially dependent couplings where a linearized metric emerges naturally as a way of efficiently encoding the field theory entanglement: by demanding that Einstein’s equations coupled to the bulk scalar field are satisfied, we show that EE can be calculated as the area of this metric. Not only does this show a direct emergence of a higher dimensional gravitational theory from any CFT, it allows for effective evaluation of the the integrals required to calculate EE perturbativly. Our results can also be interpreted as relating the non-locality of the modular hamiltonian for a spherical region in non-CFTs and the non-locality of the holographic bulk to boundary map.
This thesis studies non-locality in quantum gravity from two directions. The first concerns detection: in AdS/CFT, the gravitational Hamiltonian is a boundary observable, and its correlator with a bulk operator can be nonzero at spacelike separation. We develop a single-copy boundary protocol that exploits this structure to detect a bulk excitation before any causal signal has reached the boundary. The protocol backreacts by inducing an uncertainty in the relative bulk-boundary time shift, and we show that this backreaction controls the tradeoff between detection speed and precision. The protocol fails when the bulk operator can be dressed to commute with the boundary Hamiltonian, a condition satisfied by black hole microstates. We introduce two novel dressed-operator constructions that interpolate between holographic accessibility and effective bulk locality: an emergent clock built from the energy level spacing, and an entanglement-based dressing to an external observer via a quantum wormhole. The second part concerns transport. We study two coupled critical transverse-field Ising chains and show that this system, which has no known geometric dual, exhibits several signatures of traversable wormhole transport: a thermofield-double-like ground state, coherent left-right transfer with a timescale controlled by the Ising CFT scaling dimension, and entanglement dynamics that track the signal.
The AdS/CFT correspondence, a remarkable duality between certain gravitational theories in anti-de Sitter (AdS) spacetime and quantum field theories with conformal symmetry (CFT), has had a profound effect on the development of theoretical physics in the past two decades. Recently, many connections of AdS/CFT to quantum information theory have been found, in particular by providing gravitationally dual descriptions of various entanglement measures. Understanding these manifestions of AdS/CFT --- or more generally, the conjectured holographic principle encompassing it --- requires the combination of tools from both high-energy theory and quantum information physics. In this cumulative thesis, the convergence between these two fields is approached from two fronts: First, by calculations within the dual gravitational theory, and second, using a tensor network ansatz to describe the quantum states suspected to possess such a gravitational description. In the first approach, using the gravitational side of AdS/CFT, entanglement entropies of complicated 2+1-dimensional excited CFTs are computed, thus showing how the holographic approach provides access to systems previously out of reach of practical methods, while introducing new numerical methods that this approach necessitates. The second approach is given by tensor networks, a highly successful ansatz for computing properties of one- and two-dimensional quantum systems. Efficiently computable classes of tensor networks are tested in their ability to represent simple holographic systems, successfully reproducing both hyperbolic geometrical features as well as critical boundary states. In addition, the general properties of tensor networks on regular hyperbolic tesselations are considered, leading to new connections to models not previously considered in the context of holography. This interplay of different approaches to quantum information holography showcases the richness of this new field and suggests that a wide range of physical phenomena is accessible via the new tools now at our disposal.
Conventional understandings of quantum theory hold that measurements change the state of an observed system following the Lüders update rule. Textbooks describe the application of this idea to non-relativistic systems, but extensions to relativistic and gravitating systems encounter subtleties. One consistent approach is via detector-based measurements. We study the effects of such measurements in a CFT with a holographic dual. We work out the boundary space-time regions associated to a Lüders update and how the outcome extends to modifications of the bulk gravity state. We explore information-theoretic consequences of this picture, and relate the information extracted by a measurement to updates of the semiclassical parameters of the bulk state.
Holographic quantum-error correcting codes are models of bulk/boundary dualities such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where a higher-dimensional bulk geometry is associated with the code's logical degrees of freedom. Previous discrete holographic codes based on tensor networks have reproduced the general code properties expected from continuum AdS/CFT, such as complementary recovery. However, the boundary states of such tensor networks typically do not exhibit the expected correlation functions of CFT boundary states. In this work, we show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states. Furthermore, these codes exhibit a state-dependent breakdown of complementary recovery as expected from AdS/CFT under small quantum gravity corrections.