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In this paper, we develop a novel way to perturbatively calculate Renyi relative divergences $D_{gamma}(rho|| sigma) ={rm tr} rho^{gamma} sigma^{1-gamma}$ and related quantities without using replica trick as well as analytic continuation. We explicitly determine the form of the perturbative term at any order by an integral along the modular flow of the unperturbed state. By applying the prescription to a class of reduced density matrices in conformal field theory, we find that the second order term of certain linear combination of the divergences has a holographic expression in terms of bulk symplectic form, which is a one parameter generalization of the statement Fisher information = Bulk canonical energy.
Quantum Renyi relative entropies provide a one-parameter family of distances between density matrices, which generalizes the relative entropy and the fidelity. We study these measures for renormalization group flows in quantum field theory. We derive
Collinear and soft divergences in perturbative quantum gravity are investigated to arbitrary orders in amplitudes for wide-angle scattering, using methods developed for gauge theories. We show that collinear singularities cancel when all such diverge
We holographically compute the Renyi relative divergence $D_{alpha} (rho_{+} || rho_{-})$ between two density matrices $rho_{+}, ; rho_{-}$ prepared by path integrals with constant background fields $lambda_{pm}$ coupled to a marginal operator in JT
In this thesis we investigate some aspects of quantum field theories from a holographic perspective. In the first chapters we examine in detail a one-paremeter family of three-dimensional gauge theories by means of their type IIA gravity duals. We an
For $alpha,z>0$ with $alpha e1$, motivated by comparison between different kinds of Renyi divergences in quantum information, we consider log-majorization between the matrix functions begin{align*} P_alpha(A,B)&:=B^{1/2}(B^{-1/2}AB^{-1/2})^alpha B^{1