Related papers: From sources to initial data and back again: on bu…
In this thesis we apply techniques from quantum information theory to study quantum gravity within the framework of the anti-de Sitter / conformal field theory correspondence (AdS/CFT). Through AdS/CFT, progress has been made in…
Ab initio simulations are capable of providing detailed information of material behavior at the nanoscale. Simulating experimentally relevant situations is, however, often computationally intense. Using hybrid approaches between ab initio…
Quantum information processing exploits all the features quantum mechanics offers. Among them there is the possibility to induce nonlinear maps on a quantum system by involving two or more identical copies of the given system in the same…
We review methods of data analysis for biophysical data with a special emphasis on single molecule applications. Our review is intended for anyone, from student to established researcher. For someone just getting started, we focus on…
Quantum coherence is one of the fundamental aspects distinguishing classical and quantum theories. Coherence between different energy eigenstates is particularly important, as it serves as a valuable resource under the law of energy…
The AdS/CFT correspondence states an equivalence between a quantum gravitational theory in a (d+1)-dimensional anti-de Sitter spacetime (AdS$_{d+1}$) and a d-dimensional conformal field theory (CFT$_{d}$). The CFT$_{d}$ lives on the…
We resolve the entropy problem in the AdS$_3$/CFT correspondence by introducing both the normalizable and non-normalizable bulk modes. On the boundary, the normalizable Liouville states gives us $c=1$ conformal field theory(CFT), whereas…
We discuss information loss from black hole physics in AdS$_3$, focusing on two sharp signatures infecting CFT$_2$ correlators at large central charge $c$: 'forbidden singularities' arising from Euclidean-time periodicity due to the…
In a recent work, Ringstr\"om proposed a geometric notion of initial data on big bang singularities. Moreover, he conjectured that initial data on the singularity could be used to parameterize quiescent solutions to Einstein's equations;…
This paper contributes to the study of large data problems for $C^1$ solutions of the relativistic Euler equations. In the $(1+1)$-dimensional spacetime setting, if the initial data are away from vacuum, a key difficulty in proving the…
We introduce a task that we call partial decoupling, in which a bipartite quantum state is transformed by a unitary operation on one of the two subsystems and then is subject to the action of a quantum channel. We assume that the subsystem…
We show that it is possible to clone quantum states to arbitrary accuracy in the presence of a Deutschian closed timelike curve (D-CTC), with a fidelity converging to one in the limit as the dimension of the CTC system becomes large---thus…
We study the fundamentals of quantum field theory on a rigid de Sitter space. We show that the perturbative expansion of late-time correlation functions to all orders can be equivalently generated by a non-unitary Lagrangian on a Euclidean…
S-matrix elements in flat space can be obtained from a large AdS-radius limit of certain CFT correlators. We present a method for constructing CFT operators which create incoming and outgoing scattering states in flat space. This is done by…
We introduce a class of singular partial differential equations, the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First of all, we analyze a…
In this paper, the asymptotic distributions of estimators for the regularized functional canonical correlation and variates of the population are derived. The method is based on the possibility of expressing these regularized quantities as…
We study the equilibration properties of isolated ergodic quantum systems initially prepared in a cat state, i.e a macroscopic quantum superposition of states. Our main result consists in showing that, even though decoherence is at work in…
Except for small molecules, it is impossible to solve many electrons systems without imposing severe approximations. If the configuration interaction approaches (CI) or Coupled Clusters techniques \cite{FuldeBook} are applicable for…
In this paper, we address the problem how to represent a classical data distribution in a quantum system. The proposed method is to learn quantum Hamiltonian that is such that its ground state approximates the given classical distribution.…
We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual…