Related papers: Conditional mutual information and self-commutator
In quantum information theory it is generally accepted that quantum mutual information is an information-theoretic measure of total correlations of a bipartite quantum state. We argue that there exist quantum states for which quantum mutual…
Correlations disguised in various forms underlie a host of important phenomena in classical and quantum systems, such as information and energy exchanges. The quantum mutual information and the norm of the correlation matrix are both…
Estimating mutual information (MI) from samples is a fundamental problem in statistics, machine learning, and data analysis. Recently it was shown that a popular class of non-parametric MI estimators perform very poorly for strongly…
Given a pair of predictor variables and a response variable, how much information do the predictors have about the response, and how is this information distributed between unique, redundant, and synergistic components? Recent work has…
We correct claims about lower bounds on mutual information (MI) between real-valued random variables made in A. Kraskov {\it et al.}, Phys. Rev. E {\bf 69}, 066138 (2004). We show that non-trivial lower bounds on MI in terms of linear…
The fundamental concepts underlying in Markov networks are the conditional independence and the set of rules called Markov properties that translates conditional independence constraints into graphs. In this article we introduce the concept…
We prove continuity of quantum conditional information $S(\rho^{12}| \rho^2)$ with respect to the uniform convergence of states and obtain a bound which is independent of the dimension of the second party. This can, e.g., be used to prove…
We give two strengthenings of an inequality for the quantum conditional mutual information of a tripartite quantum state recently proved by Fawzi and Renner, connecting it with the ability to reconstruct the state from its bipartite…
In this paper we investigate the notion of conditional independence and prove several information inequalities for conditionally independent random variables.
We derive a well-defined renormalized version of mutual information that allows to estimate the dependence between continuous random variables in the important case when one is deterministically dependent on the other. This is the situation…
Relativistic quantum information combines the informational approach to understanding and using quantum mechanics systems - quantum information - with the relativistic view of the universe. In this introductory review we examine key results…
We introduce the Conditional Mutual Information (CMI) for the estimation of the Markov chain order. For a Markov chain of $K$ symbols, we define CMI of order $m$, $I_c(m)$, as the mutual information of two variables in the chain being $m$…
Given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the "partial information" one system needs conditioned…
The conditional mutual information quantifies the conditional dependence of two random variables. It has numerous applications; it forms, for example, part of the definition of transfer entropy, a common measure of the causal relationship…
In previous papers, we expressed the Entanglement of Formation in terms of Conditional Mutual Information (CMI). In this brief paper, we express the Entanglement of Distillation in terms of CMI.
Spontaneous synchronization is a fundamental phenomenon, important in many theoretical studies and applications. Recently this effect has been analyzed and observed in a number of physical systems close to the quantum mechanical regime. In…
We use a well known model (T. Vicsek et al. Phys Rev Lett 15, 1226 (1995)) for flocking to test mutual information as a tool for detecting order-disorder transitions, in particular when observations of the system are limited. We show that…
In this paper and a companion paper, we attempt to systematically investigate the possibility that the concept of information may enable a derivation of the quantum formalism from a set of physically comprehensible postulates. To do so, we…
This correspondence studies an estimator of the conditional support of a distribution underlying a set of i.i.d. observations. The relation with mutual information is shown via an extension of Fano's theorem in combination with a…
We investigate a two-qubit system to understand the relationship between concurrence and mutual information, where the former determines the amount of quantum entanglement, whereas the latter is its classical residue after performing local…