Quantum information, computation and communication (Q5891707)

This book is a brief introduction to the interesting fields of quantum information, computation and communication, which are covered in three parts. The first part starts with a short introduction to quantum gates and measurement. Afterwards, several qubit implementations are presented: These are atoms in laser fields (also discussing time-dependent perturbation theory, Rabi flopping and Raman transitions), spins in magnetic fields (including the transformation into a rotating frame and spin echo measurements), and photons, where qubit encodings in spatial and polarization degrees of freedom are touched. Chapter 5 treats two qubits, after a brief introduction to the tensor product, two-qubit gates and entanglement are explored. Finally, Chapter 6 formally discusses measurement in arbitrary bases, the no-cloning theorem and shortly also local operations. The second part stars with the DiVincenzo criteria, followed by an exposition of the elementary quantum algorithms (including also a discussion on quantum error correction and decoherence-free subspaces). Chapter 9 contains more advanced algorithms and distinguishes period-finding algorithms and search algorithms. It closes with a brief discussion on quantum simulation by trotterization. Chapters 10 and 11 introduce techniques and experimental implementation for trapped ions/atoms and NMR, respectively. They start by introducing the physical realization, discuss how a universal quantum logic is implemented and also initialization and readout. Finally, Chapter 12 discusses the scaling prospectives of these (and a few other) implementations as the number of qubits increases. The third part starts with a brief exposition of classical information theory by introducing the Shannon entropy, mutual information and channel capacities. Chapter 14 provides the quantum counterpart, which requires the introduction of density operator, the reduced density matrix, the von-Neumann entropy and also quantum channels with Kraus operators. Actual quantum communication is presented in Chapter 15, which discusses the creation of entangled photon pairs via parametric down-conversion, dense coding and quantum teleportation. Chapter 16 discusses the Bell inequalities and the corresponding experiments by A. Aspect and also provides a short summary of possible loopholes. In addition, it discusses the relevance of GHZ-states in this context. The last chapter discusses secure classical (Vernam cipher) and quantum (BB84, Ekert91) cryptography protocols. An appendix provides the basic techniques used in quantum mechanics.NEWLINENEWLINEThe first two parts can be read independently, whereas the third part requires information from the first. The book does not waste time with trivialities and at the same time is not over-sophisticated. It is of course too short to discuss the problems in too great detail, but newcomers will enjoy that each chapter ends with a section suggesting further reading for each topic and a few exercises. A nice feature is that it makes many references to common experimental techniques, from which a theoretician may profit. It is recommendable as a first overview to students and scientists with a little background in quantum mechanics.