This book is a new non-traditional theoretical reference for communication professionals and statisticians specializing in information theory.

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## Data processing using information theory functionals

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Email address subscribed successfully. A activation email has been sent to you. What is the expected value of the condition number of this random matrix? The first part is a joint work with Aram Harrow and Matthew Hastings and has appeared as arxiv preprint Time permitting, we will discuss in more detail relaations between the operator-valued free, Boolean and monotone central limits. This is joint work with Mihai V. Popa and Victor Vinnikov. Hasting's counterexamples on the minimum output entropy additivity conjecture by measure concentration. In Hastings reported a randomized construction of channels violating the minimum output entropy additivity conjecture.

In this talk we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. We prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension.

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In this talk I will describe how random matrix theory and free probability theory and in particular, results of Haagerup and Thorbjornsen can give insight into the problem of understanding all possible eigenvalues of the output of important classes of random quantum channels. I will also describe applications to the minimum output entropy additivity problems. We introduce a class of probability spaces whose objects are infinite graphs and whose probability distributions are obtained as limits of distributions for finite graphs.

The notions of Hausdorff and spectral dimension for such ensembles are defined and some results on their value in koncrete examples, such as random trees, will be described. The headline result of this talk is that, based on plausible complexity-theoretic assumptions, many properties of quantum channels are computationally hard to approximate.

The proof of this claim has two main ingredients.

First, I show how many channel problems can be fruitfully recast in the language of two-prover quantum Merlin-Arther games which I'll define during the talk. Second, the main technical contribution is a procedure that takes two copies of a multipartite quantum state and estimates whether or not it is close to a product state.

## Finite-block-length analysis in classical and quantum information theory

In this talk we will give an overview of how different probabilistic and quantum probabilistic techniques can be used to find Bell inequalities with large violation. This will include previous result on violation for tripartite systems and more recent results with Palazuelos on probabilities for bipartite systems.

Quite surprisingly the latest results are the most elementary, but lead to some rather surprsing independence of entropy and large violation. One of the major problems hindering progress in quantum many body systems is the inability to describe the spectrum of the Hamiltonian.

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The spectrum corresponds to the energy spectrum of the problem and is of out-most importance in accounting for the physical properties of the system. A perceived difficulty is the exponential growth of the Hamiltonian with the number of particles involved.

### Researchers list

New Releases. Even with such generality the authors have managed to successfully reach a highly unconventional but very fertile exposition rendering new insights into many problems. Product details Format Hardback pages Dimensions x x Other books in this series. Add to basket. Modelling Extremal Events Paul Embrechts. Stochastic Calculus and Financial Applications J. Discretization of Processes Jean Jacod. Fundamentals of Stochastic Filtering Alan Bain. Stochastic Controls Jiongmin Yong. Optimal Stopping Rules Albert N. Table of contents 1 Source Coding. This book presents useful and important concepts in information theory arising from original ideas of the author