Related papers: Smooth Max-Information as One-Shot Generalization …
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…
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…
The chain rule for the Shannon and von Neumann entropy, which relates the total entropy of a system to the entropies of its parts, is of central importance to information theory. Here we consider the chain rule for the more general smooth…
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…
Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected…
One-shot information theory entertains a plethora of entropic quantities, such as the smooth max-divergence, hypothesis testing divergence and information spectrum divergence, that characterize various operational tasks and are used to…
The precise one-shot characterisation of operational tasks in classical and quantum information theory relies on different forms of smooth entropic quantities. A particularly important connection is between the hypothesis testing relative…
In this work we derive a number of chain rules for mutual information quantities, suitable for analyzing quantum cryptography with imperfect devices that leak additional information to an adversary. First, we derive a chain rule between…
Mutual information is used as a purely geometrical regularization of entanglement entropy applicable to any QFT. A coefficient in the mutual information between concentric circular entangling surfaces gives a precise universal prescription…
Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…
We present an iterative algorithm based on semidefinite programming (SDP) for computing the quantum smooth max-mutual information $I^\varepsilon_{\max}(\rho_{AB})$ of bipartite quantum states in any dimension. The algorithm is accurate if a…
We introduce a new operational technique for deriving chain rules for general information theoretic quantities. This technique is very different from the popular (and in some cases fairly involved) methods like SDP formulation and operator…
Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic…
Mutual information is widely applied to learn latent representations of observations, whilst its implication in classification neural networks remain to be better explained. We show that optimising the parameters of classification neural…
We study entanglement-assisted quantum and classical communication over a single use of a quantum channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. We obtain characterizations of…
Renormalization is an essential technique in field-theoretic descriptions of natural phenomena, where the absence of a UV-complete description yields an abundance of divergent quantities. While the renormalization prescription has been…
The von Neumann entropy of an $n$-partite system $A_1^n$ given a system $B$ can be written as the sum of the von Neumann entropies of the individual subsystems $A_k$ given $A_1^{k-1}$ and $B$. While it is known that such a chain rule does…
This paper presents expression of mutual information that defines the information gain in planning of sensing resources, when the goal is to reduce the forecast uncertainty of some quantities of interest and the system dynamics is described…
Using the relative entropy of total correlation, we derive an expression relating the mutual information of $n$-partite pure states to the sum of the mutual informations and entropies of its marginals and analyze some of its implications.…
Two new relative entropy quantities, called the min- and max-relative entropies, are introduced and their properties are investigated. The well-known min- and max- entropies, introduced by Renner, are obtained from these. We define a new…