Mathematics of Quantum Computation [Hardcover]

Among the most exciting developments in science today is the design and construction of the quantum computer. Its realization will be the result of multidisciplinary efforts, but ultimately, it is mathematics that lies at the heart of theoretical quantum computer science.

Mathematics of Quantum Computation brings together leading computer scientists, mathematicians, and physicists to provide the first interdisciplinary but mathematically focused exploration of the field's foundations and state of the art. Each section of the book addresses an area of major research, and does so with introductory material that brings newcomers quickly up to speed. Chapters that are more advanced include recent developments not yet published in the open literature.

Information technology will inevitably enter into the realm of quantum mechanics, and, more than all the atomic, molecular, optical, and nanotechnology advances, it is the device-independent mathematics that is the foundation of quantum computer and information science. Mathematics of Quantum Computation offers the first up-to-date coverage that has the technical depth and breadth needed by those interested in the challenges being confronted at the frontiers of research.Preface
PART I: QUANTUM ENTANGLEMENT
ALGEBRAIC MEASURES OF ENTANGLEMENT, Jean-Luc Brylinski
Introduction
Rank of a Tensor
Tensors in (C 2)?2
Tensors in (C 2)?3
Tensors in (C 2)?4
KINEMATICS OF QUBIT PAIRS, Berthold-Geor Englert and Nasser Metwally
Introduction
Basic Classification of States
Projectors and Subspaces
Positivity and Separability
Lewenstein-Sanpera Decompositions
Examples
INVARIANTS FOR MULTIPLE QUBITS: The Case of 3 Qubits, David A. Meyer and Noland Wallach
Introduction
Invariants for Compact Lie Groups
The Simplest Cases
The Case of Three Qubits
A Basic Set of Invariants for Three Qubits