We generalize our results both to the case of higher dimensional subsystems and also to more than three subsystems, for all of which we show that, typically, two randomly chosen pure states cannot be converted into each other by means of LOCC, not even with a small probability of success. In particular, we show that the W state retains maximally bipartite entanglement when any one of the three qubits is traced out. When applied to pure states of a three-qubit system, this approach reveals the existence of two inequivalent kinds of genuine tripartite entanglement, for which the GHZ state and a W state appear as remarkable representatives. Accordingly, we say that two states have the same kind of entanglement if both of them can be obtained from the other by means of local operations and classical communcication (LOCC) with nonzero probability. This classification concerns the entanglement properties of a single copy of the state. Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. © 2010 by World Scientific Publishing Co. The new research topics added to this second edition are: entanglement, teleportation, Berry phase, Morse oscillator, Magnus expansion, wavelets, Pauli and Clifford groups, coupled Bose-Fermi systems, super-Lie algebras, etc. Modern developments in quantum theory are covered extensively, beyond the standard quantum mechanical techniques. Selected problems have also been implemented using two other popular packages - Mathematica and Maple - while some problems are implemented in C++. Throughout, the sample programs and their outputs are accompanied with explanatory text of the underlying mathematics and physics explained in detail. This book collects standard and advanced methods in quantum mechanics and implements them using SymbolicC++ and Maxima, two popular computer algebra packages. For example, the manipulations of noncommutative operators, differentiation and integration can now be carried out algebraically by the computer algebra package. Nowadays, the labor of scientific computation has been greatly eased by the advent of computer algebra packages, which do not merely perform number crunching, but also enable users to manipulate algebraic expressions and equations symbolically. Solving problems in quantum mechanics is an essential skill and research activity for physicists, mathematicians, engineers and others. © 2012 by World Scientific Publishing Co. Almost all problems are solved in detail and most of the problems are self-contained.
The topics range in difficulty from elementary to advanced. All the important concepts and topics such as quantum gates and quantum circuits, product Hilbert spaces, entanglement and entanglement measures, deportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gate, von Neumann entropy, quantum cryptography, quantum error corrections, number states and Bose operators, coherent states, squeezed states, Gaussian states, POVM measurement, quantum optics networks, beam splitter, phase shifter and Kerr Hamilton operator are included. This book supplies a huge collection of problems in quantum computing and quantum information together with their detailed solutions, which will prove to be invaluable to students as well as researchers in these fields. Entanglement, teleportation and the possibility of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to this new interest. Quantum computing and quantum information are two of the fastest growing and most exciting research fields in physics.
© 2011 by World Scientific Publishing Co. New topics added to the second edition are: braid-like relations, Clebsch-Gordan expansion, nearest Kronecker product, Clifford and Pauli group, universal enveloping algebra, computer algebra and Kronecker product. The book is well suited for pure and applied mathematicians as well as theoretical physicists and engineers. Computer algebra applications are also given. A key feature of the book is the many detailed worked-out examples. The Kronecker product has widespread applications in signal processing, discrete wavelets, statistical physics, computer graphics, fractals, quantum mechanics and quantum computing. Emphasis is placed on the Kronecker product and tensor product. Besides the standard techniques for linear and multilinear algebra many advanced topics are included. This book provides a self-contained and accessible introduction to linear and multilinear algebra.
0 kommentar(er)
