= ASSESSMENT OF CURRENT RESULTS AND OUTLOOK ON FUTURE EFFORTS =

### QUANTUM INFORMATION SCIENCE THEORY

#### INTRODUCTION

The development of quantum information science (QIS) was initially driven by theoretical work of scientists working on the boundary between Physics, Computer Science, Mathematics, and Information Theory. In the early stages of the development of QIS, theoretical work has often been far ahead of experimental realization of these ideas. At the same time, theory has provided a number of proposals of how to implement basic ideas and concepts from link building service quantum information in specific physical systems. These ideas are now forming the basis for successful experimental work in the laboratory, driving forward the development of tools that will form the basis for all loan modification future technologies which employ, control and manipulate matter and radiation at the quantum level.

Today one can observe a broad and growing spectrum of theoretical activities. Investigations include, to name just a few examples,

- basic concepts such as entanglement and decoherence,
- characterization and quantification of (two- & multi-party) entanglement,
- novel quantum algorithms and communication protocols,
- capacities of noisy quantum communication channels,
- optimization of protocols for quantum cryptography,
- new computer models and architectures.

Another important class of theoretical work is concerned with implementations of these abstract concepts in real physical systems.

In fact, many of these theoretical proposals have formed the starting point as well as the guide for experimental work in the laboratories, as is described in the other sections of this document. Last, but not least, the transfer of concepts from quantum information theory to other fields of physics such as condensed matter physics or quantum field theory has proved fruitful and has attracted considerable interest recently.

It is important to realize that these activities are often interdisciplinary in nature and span a broad spectrum of research in which the different activities are benefiting from each other to a large degree. Thus it does not seem to be advisable to concentrate research on too narrowly defined topics only. Theory groups in Europe have been consistently delivered international leadership in the entire spectrum of research (see more below). This has been facilitated by a flexible and topically broad financing on European and national levels in the past.

In the following we give a brief outline of the current status and the perspectives of the main areas of quantum information theory.