Related papers: Computational relative entropy
We initiate the study of computational entropy in the quantum setting. We investigate to what extent the classical notions of computational entropy generalize to the quantum setting, and whether quantum analogues of classical theorems hold.…
Computational pseudorandomness studies the extent to which a random variable $\bf{Z}$ looks like the uniform distribution according to a class of tests $\cal{F}$. Computational entropy generalizes computational pseudorandomness by studying…
In this paper, we provide a simple framework for deriving one-shot achievable bounds for some problems in quantum information theory. Our framework is based on the joint convexity of the exponential of the collision relative entropy, and is…
Quantum theory imposes fundamental limitations to the amount of information that can be carried by any quantum system. On the one hand, Holevo bound rules out the possibility to encode more information in a quantum system than in its…
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability…
Quantum filtering is a signal processing technique that estimates the posterior state of a quantum system under continuous measurements and has become a standard tool in quantum information processing, with applications in quantum state…
In modern quantum information theory one deals with an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime.…
Rate-distortion theory provides bounds for compressing data produced by an information source to a specified encoding rate that is strictly less than the source's entropy. This necessarily entails some loss, or distortion, between the…
This paper systematically develops the resource theory of asymmetric distinguishability, as initiated roughly a decade ago [K. Matsumoto, arXiv:1010.1030 (2010)]. The key constituents of this resource theory are quantum boxes, consisting of…
The conditional entropy power inequality is a fundamental inequality in information theory, stating that the conditional entropy of the sum of two conditionally independent vector-valued random variables each with an assigned conditional…
We consider the analysis of probability distributions through their associated covariance operators from reproducing kernel Hilbert spaces. We show that the von Neumann entropy and relative entropy of these operators are intimately related…
This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states. These measures should have important appli- cations in…
The first step in quantum information theory is the identification of entanglement as a valuable resource. The next step is learning how to exploit this resource efficiently. We learn how to exploit entanglement efficiently by applying…
Quantum relative entropy, a quantum generalization of the renowned Kullback-Leibler divergence, serves as a fundamental measure of the distinguishability between quantum states and plays a pivotal role in quantum information science.…
Relative entropy is the standard measure of distinguishability in classical and quantum information theory. In the classical case, its loss under channels admits an exact chain rule, while in the quantum case only asymptotic, regularized…
Fundamental limits on the controllability of quantum mechanical systems are discussed in the light of quantum information theory. It is shown that the amount of entropy-reduction that can be extracted from a quantum system by feedback…
A new finite form of de Finetti's representation theorem is established using elementary information-theoretic tools. The distribution of the first $k$ random variables in an exchangeable vector of $n\geq k$ random variables is close to a…
Distinguishability is fundamental to information theory and extends naturally to quantum systems. While quantum state discrimination is well understood, quantum channel discrimination remains challenging due to the dynamic nature of…
Classical probabilistic models of (noisy) quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources…
To explain conceptual gap between classical/quantum and other, hypothetical descriptions of world, several principles has been proposed. So far, all these principles have not explicitly included the uncertainty relation. Here we introduce…