相关论文: From sources to initial data and back again: on bu…
We interpret appropriate families of Euclidean wormhole solutions of AdS$_3$ gravity in individual 2d CFTs as replica wormholes described by branching around the time-symmetric apparent horizons of black holes sourced by the backreaction of…
Within AdS/CFT, we establish a general procedure for obtaining the leading singularity of two-point correlators involving operator insertions at different times. The procedure obtained is applied to operators dual to a scalar field which…
Recent advancements in quantum technologies, particularly in quantum sensing and simulation, have facilitated the generation and analysis of inherently quantum data. This progress underscores the necessity for developing efficient and…
Time-varying non-Euclidean random objects are playing a growing role in modern data analysis, and periodicity is a fundamental characteristic of time-varying data. However, quantifying periodicity in general non-Euclidean random objects…
Originally, quantum probability theory was developed to analyze statistical phenomena in quantum systems, where classical probability theory does not apply, because the lattice of measurable sets is not necessarily distributive. On the…
These notes introduce a handful of core ideas from quantum information science that figure prominently in modern research on quantum gravity. The central concept that forms the base of these notes is that of a quantum channel; that is, the…
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can…
We survey approaches to nonrelativistic density functional theory (DFT) for nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using…
We consider admissible weak solutions to the compressible Euler system with source terms, which include rotating shallow water system and the Euler system with damping as special examples. In the case of anti-symmetric sources such as…
An important insight from the study of AdS/CFT is that bulk locality can be derived from crossing symmetry of the boundary CFT. In this paper, we take the first steps in extending this statement to de Sitter background by demonstrating how…
We examine the inference of quantum density operators from incomplete information by means of the maximization of general non-additive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1/2 system,…
Motivated by the holographic principle, within the context of the AdS/CFT Correspondence in the large t'Hooft limit, we investigate how the geometry of certain highly symmetric bulk spacetimes can be recovered given information of physical…
Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for generating unbiased and independent samples from graphical models remains an active research…
Euclidean field theories admit more general deformations than usually discussed in quantum field theories because of mixing between rotational symmetry and internal symmetry (a.k.a topological twist). Such deformations may be relevant, and…
We present the first comprehensive Lean 4 formalization of statistical learning theory (SLT) grounded in empirical process theory. Our end-to-end formal infrastructure implement the missing contents in latest Lean 4 Mathlib library,…
In this paper we construct CFT states describing a putative holographic dual to local excitations in the three-dimensional de Sitter space (dS), called the bulk local states. We find that the conjugation operation in dS$_3/$CFT$_2$ is…
Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…
These lectures are designed to provide a general introduction to the Einstein-Vlasov system and to the global Cauchy problem for these equations. To start with some general facts are collected and a local existence theorem for the Cauchy…
An optical source that produces single photon pulses on demand has potential applications in linear optics quantum computation, provided that stringent requirements on indistinguishability and collection efficiency of the generated photons…
The necessary information for specifying a complex system may not be completely accessible to us, i.e., to mathematical treatments. This is not to be confounded with the incompleteness of our knowledge about whatever systems or nature,…