Related papers: On the Second-Order Asymptotics of the Partially S…
We address the problem of exact and approximate transformation of quantum dichotomies in the asymptotic regime, i.e., the existence of a quantum channel $\mathcal E$ mapping $\rho_1^{\otimes n}$ into $\rho_2^{\otimes R_nn}$ with an error…
We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the specified error…
In classical and quantum information theory, operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two…
In quantum state redistribution as introduced in [Luo and Devetak (2009)] and [Devetak and Yard (2008)], there are four systems of interest: the $A$ system held by Alice, the $B$ system held by Bob, the $C$ system that is to be transmitted…
In quantum metrology, information about unknown parameters $\mathbf{\theta} = (\theta_1,\ldots,\theta_M)$ is accessed by measuring probe states $\hat{\rho}_{\mathbf{\theta}}$. In experimental settings where copies of…
We compute exact second-order asymptotics for the cost of an optimal solution to the entropic optimal transport problem in the continuous-to-discrete, or semi-discrete, setting. In contrast to the discrete-discrete or continuous-continuous…
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…
The entropy shows an unavoidable tendency of disorder in thermostatistics according to the second thermodynamics law. This provides a minimization entropy principle for quantum thermostatistics with the von Neumann entropy and nonextensive…
In this paper, we consider the standard quantum information decoupling, in which Alice aims to decouple her system from the environment by local operations and discarding some of her systems. To achieve an $\varepsilon$-decoupling with…
We study rates asymptotic of transformations between entangled states by local operations and classical communication and a sublinear amount of quantum communication. It is known that additive asymptotically continuous entanglement measures…
We study asymptotic state transformations in continuous variable quantum resource theories. In particular, we prove that monotones displaying lower semicontinuity and strong superadditivity can be used to bound asymptotic transformation…
We give an operational meaning to the min-entropy of a quantum state as a resource measure for various interconnected tasks. In particular, we show that the min-entropy without smoothing measures the amount of quantum information that can…
Motivated by a problem arising from Density Functional Theory, we provide the sharp next-order asymptotics for a class of multimarginal optimal transport problems with cost given by singular, long-range pairwise interaction potentials. More…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
We study the first- and second-order asymptotics of covert communication over binary-input DMC for three different covertness metrics and under maximum probability of error constraint. When covertness is measured in terms of the relative…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
We give sufficient conditions for the asymptotic normality of linear combinations of order statistics (L-statistics) in the case of simple random samples without replacement. In the first case, restrictions are imposed on the weights of…
Integrated task and motion planning problems describe a multi-modal state space, which is often abstracted as a set of smooth manifolds that are connected via sets of transitions states. One approach to solving such problems is to sample…
We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the…
Given a mixture of states, finding a way to optimally discriminate its elements is a prominent problem in quantum communication theory. In this paper, we will address mixtures of density operators that are unitarily equivalent via elements…