# Mathematical Aspects of Quantum Information Science

Quantum information science is a rapidly growing research area. The study concerns the use of quantum properties in constructing fast computing devices and designing secure communicating schemes. While the advance of quantum information science promises far-reaching implications, there are many open theoretical questions and experimental challenges that must be overcome. For instance, one has to develop the theory and techniques for quantum control, quantum error correction, quantum tomography, etc. to deal with problems and make use of resources arising from quantum phenomena such as entanglement and decoherence.

Quantum information science research is inherently multi-disciplinary, as it draws significantly on aspects of mathematics, physics, computer science, information theory, engineering and chemistry. The common language of mathematics provides a foundation on which quantum information scientists from different backgrounds can communicate ideas. Although mathematicians have been involved in quantum information research from the early breakthroughs in the 1980’s, the rapid maturation of the area has generated new challenges. For instance, it is known that all quantum operations correspond to trace preserving completely positive (TPCP) linear maps, and researchers have established deep theoretical results such as the Stinespring dilation theorem, and the operator sum representations for finite dimensional CP maps. Furthermore, recent developments involve increasingly sophisticated techniques from a wide range of mathematics areas such as Lie theory, convex geometry, knots theory, representation theory, etc.

It is our hope that the proposed workshop will bring researchers interested in the topic together to achieve the following goals:

1. To promote collaborations among different research groups to study central problems in quantum information science,

2. To solve important open problems, and develop results and techniques in quantum information science,

3. To develop the work force in quantum information by doing research with undergraduate and graduate students.

**Organizers**

Name | University |
---|---|

Shiu-Yuen Cheng | Tsinghua University, China |

Man-Duen Choi | University of Toronto, Canada |

Shangquan Bu | Tsinghua University, China |

Jianlian Cui | Tsinghua University, China |

Jinchuan Hou | Taiyuan University of Technology, China |

Chi-Kwong Li | College of William & Mary, USA |

Guilu Long | Tsinghua University, China |