Related papers: Quantum Shannon Theory
This series of introductory lectures consists of two parts. In the first part, I rapidly review the basic notions of quantum physics and many primitives of quantum information (i.e. notions that one must be somehow familiar with in the…
Distributed quantum information processing is a promising platform for scaling up quantum information processing, where small- and intermediate-scale quantum devices are connected by a network of quantum channels for communicating quantum…
The work presented here extends upon the best known universal quantum circuit, the Quantum Shannon Decomposition proposed in [Vivek V. Shende, Stephen S. Bullock and Igor Markov, Synthesis of Quantum Logic Circuits, IEEE Trans.…
In this paper alternative formulations of the conventional uncertainty relation are studied in the context of decoherent histories. The results are given in terms of Shannon information. A variety of methods are developed to evaluate the…
The recent development of quantum computing, which uses entanglement, superposition, and other quantum fundamental concepts, can provide substantial processing advantages over traditional computing. These quantum features help solve many…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start…
The decoupling technique is a fundamental tool in quantum information theory with applications ranging from quantum thermodynamics to quantum many body physics to the study of black hole radiation. In this work we introduce the notion of…
Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately it has emerged that they are in fact intimately related. In this…
We revisit the quantum reverse Shannon theorem, a central result in quantum information theory that characterizes the resources needed to simulate quantum channels when entanglement is freely available. We derive a universal additive upper…
This article is a snap-shot of a web site, which has been collecting open problems in quantum information for several years, and documenting the progress made on these problems. By posting it we make the complete collection available in one…
Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale…
Few, if any, applications of quantum technology are as widely known as the quantum simulation of quantum matter. Consequently, many interesting questions have been sparked at the intersection of condensed matter, quantum chemistry, and…
Decoupling theorems have proven useful in various applications in the area of quantum information theory. This thesis builds upon preceding work by Fr\'{e}d\'{e}ric Dupuis [arXiv:1012.6044v1], where a general decoupling theorem is obtained…
Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while…
This is an updated version of my PhD thesis, defended at the University of Waterloo on the 2nd of April 2025, uploaded to the ArXiv with the goal of reaching a wider audience. The thesis is divided into 5 chapters, respectively containing…
This paper is an essentially self-contained and rigorous description of the fundamental principles of quantum computing from a mathematical perspective. It is intended to help mathematicians who want to get a grasp of this quickly growing…
Information complexity is the interactive analogue of Shannon's classical information theory. In recent years this field has emerged as a powerful tool for proving strong communication lower bounds, and for addressing some of the major open…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
We identify five selected open problems in the theory of quantum information, which are rather simple to formulate, were well-studied in the literature, but are technically not easy. As these problems enjoy diverse mathematical connections,…