# Fundamentals of quantum information theory

@article{Keyl2002FundamentalsOQ, title={Fundamentals of quantum information theory}, author={Michael Keyl}, journal={Physics Reports}, year={2002}, volume={369}, pages={431-548} }

Abstract In this paper we give a self-contained introduction to the conceptional and mathematical foundations of quantum information theory. In the first part we introduce the basic notions like entanglement, channels, teleportation, etc. and their mathematical description. The second part is focused on a presentation of the quantitative aspects of the theory. Topics discussed in this context include: entanglement measures, channel capacities, relations between both, additivity and continuity… Expand

#### Figures from this paper

figure 1.1 figure 1.2 figure 1.3 figure 1.4 figure 3.1 figure 3.2 figure 3.3 figure 3.4 figure 3.5 figure 3.6 figure 3.7 figure 4.1 figure 4.2 figure 4.3 figure 4.4 figure 4.5 figure 4.6 figure 4.7 figure 4.8 figure 4.9 figure 5.1 figure 5.2 figure 5.3 figure 5.4 figure 5.5 figure 5.6 figure 6.1 figure 6.2 figure 6.3 figure 6.4 figure 6.5 figure 6.6 figure 6.7 figure 6.8 figure 7.1 figure 7.2 figure 7.3 figure 7.4

#### 230 Citations

Entanglement, CP-Maps and Quantum Communications

- Computer Science
- Quantum Physics and Geometry
- 2019

This chapter introduces and discusses the notion of completely positive maps operating on observable algebras of physical systems in order to have a model to construct communication channels based on quantum processes. Expand

Vacuum Fluctuations, Geometric Modular Action and Relativistic Quantum Information Theory

- Physics
- 2005

A summary of some lines of ideas leading to model-independent frameworks of relativistic quantum field theory is given. It is followed by a discussion of the Reeh-Schlieder theorem and geometric… Expand

Some Aspects of Operator Algebras in Quantum Physics

- Mathematics, Physics
- 2016

Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the… Expand

On quantum vs. classical probability

- Mathematics, Physics
- 2007

Abstract Quantum theory shares with classical probability theory many important properties. I show that this common core regards at least the following six areas, and I provide details on each of… Expand

Introduction to quantum entanglement

- Mathematics
- 2012

This paper contains a characterization of certain aspects of bipartite quantum entanglement. We discuss relationship between entropy and entanglement, as well as qualitative and quantitative aspects… Expand

Categories of quantum and classical channels

- Mathematics, Computer Science
- Quantum Inf. Process.
- 2016

A construction that turns a category of pure state spaces and operators into a categories of observable algebras and superoperators is introduced, providing elegant abstract notions of preparation and measurement. Expand

Quantum channels and their entropic characteristics.

- Physics, Mathematics
- Reports on progress in physics. Physical Society
- 2012

A survey of the main properties of quantum channels and of their entropic characterization, with a variety of examples for finite-dimensional quantum systems, and the remarkable role of specific quantum correlations-entanglement-as a novel communication resource is stressed. Expand

Quantum Information and Relativity: An Introduction

- Physics
- 2010

Information and physics are closely and fascinatingly intertwined. Their relations become even more interesting when we leave a non-relativistic quantum mechanics for more exiting venues. My notes… Expand

Qubit quantum channels: A characteristic function approach

- Physics
- 2007

A characterization of qubit quantum channels is introduced. In analogy to what happens in the context of bosonic channels we exploit the possibility of representing the states of the system in terms… Expand

Quantum Information and Relativity Theory

- Physics
- 2004

Quantum mechanics, information theory, and relativity theory are the basic foundations of theoretical physics. The acquisition of information from a quantum system is the interface of classical and… Expand

#### References

SHOWING 1-10 OF 227 REFERENCES

Statistical structure of quantum theory

- Mathematics
- 2001

The course presents some basic concepts and rigorous results of a new scientiflc discipline { quantum information theory. It starts with a thorough reconsideration of the mathematical foundations of… Expand

Negative entropy and information in quantum mechanics

- Physics
- 1997

A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum… Expand

Coding Theorems for Quantum Channels

- Physics
- 1998

The more than thirty years old issue of the (classical) information capacity of quantum communication channels was dramatically clarified during the last years, when a number of direct quantum coding… Expand

Introduction to Quantum Computation Information

- Computer Science
- 2002

This book aims to provide a pedagogical introduction to the subjects of quantum information and computation, including non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault-tolerant quantum computation and quantum cryptography. Expand

Achievable rates for the Gaussian quantum channel

- Physics
- 2001

We study the properties of quantum stabilizer codes that embed a finite-dimensional protected code space in an infinite-dimensional Hilbert space. The stabilizer group of such a code is associated… Expand

Bibliographic guide to the foundations of quantum mechanics and quantum information

- Physics
- 2000

This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, web sites, etc.), sorted alphabetically and (some of them) classified by subject, on foundations of… Expand

The physics of quantum information: quantum cryptography, quantum teleportation, quantum computation

- Computer Science, Physics
- Physics and astronomy online library
- 2000

Leading experts from "The Physics of Quantum Information" network, initiated by the European Commission, bring together the most recent results from this emerging area of quantum technology, considering both theory and newest experiments. Expand

Unified approach to quantum capacities: towards quantum noisy coding theorem

- Mathematics, Physics
- Physical review letters
- 2000

It is shown that the rate of quantum information transmission is bounded by the maximal attainable rate of coherent information and if for any bipartite state the one-way distillable entanglement is no less than coherent information, then one obtains Shannon-like formulas for all the capacities. Expand

Limits for entanglement measures.

- Mathematics, Medicine
- Physical review letters
- 2000

It is shown that any entanglement measure E suitable for the regime of a high number of identically prepared entangled pairs satisfies ED < or = E = or = EF, where ED and EF are theEntanglement of distillation and formation, respectively. Expand

Information transmission through a noisy quantum channel

- Physics
- 1998

Noisy quantum channels may be used in many information-carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these… Expand