相关论文: Bit threads, Einstein's equations and bulk localit…
Recent research has leveraged the tractability of $T\bar T$ style deformations to formulate timelike-bounded patches of three-dimensional bulk spacetimes including $dS_3$. This proceeds by breaking the problem into two parts: a solvable…
We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…
We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that the errors…
In this note, we consider entanglement and Renyi entropies for spatial subsystems of a boundary conformal field theory (BCFT) or of a CFT in a state constructed using a Euclidean BCFT path integral. Holographic calculations suggest that…
In the long-standing quest to reconcile gravity with quantum mechanics, profound connections have been unveiled between concepts traditionally pertaining to quantum information theory, such as entanglement, and constitutive features of…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
Motivated by the theory of holographic quantum error correction in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, together with the kink transform conjecture on the bulk AdS description of boundary cocycle flow, we…
Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…
The aim of this dissertation is to clarify the structure of entanglement, a type of quantum correlations, in various quantum systems with a large number of degrees of freedom for holography between generic quantum systems and spacetimes…
Flat space holography is an open and hard problem existing several different approaches, which may finally turn out to be consistent with each other, in the literature to tackle it. Focusing on how bulk emergent spacetime is encoded in…
Deep embedding methods have influenced many areas of unsupervised learning. However, the best methods for learning hierarchical structure use non-Euclidean representations, whereas Euclidean geometry underlies the theory behind many…
We show that complementary state-specific reconstruction of logical (bulk) operators is equivalent to the existence of a quantum minimal surface prescription for physical (boundary) entropies. This significantly generalizes both sides of an…
The brick wall model is a semi-classical approach to understanding the microscopic origin of black hole entropy. We outline the formalism for the brick wall model in arbitrary number of dimensions and generalize it to include both charged…
This paper concerns the inverse scattering problem to reconstruct a locally perturbed periodic surface. Different from scattering problems with quasi-periodic incident fields and periodic surfaces, the scattered fields are no longer…
There have been many attempts to understand the statistical origin of black-hole entropy. Among them, entanglement entropy and the brick wall model are strong candidates. In this paper, first, we show that the entanglement approach reduces…
We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…
We present a geometric framework for the inverse design of smart woven fabrics composed of non-uniformly shrinking threads. A sufficiently tight weaving structure imposes strong local criteria on the material deformation and reduces the…
This article examines the inverse problem for a lossy quantum graph that is internally excited and sensed. In particular, we supply an algorithmic methodology for deducing the topology and geometric structure of the underlying metric graph.…
The inverse scattering problem for biharmonic waves, governing flexural vibrations of elastic plates, presents fundamental analytical challenges distinct from acoustic inverse problems due to the fourth-order differential operator and…
Recent advances in holography and quantum gravity have shown that CFTs with classical gravity duals can implement nonlocal quantum computation protocols that appear local from the bulk perspective. We examine the extent to which current…