This book gives an overview for practitioners and students of quantum physics and information science. Unlike other books in quantum information and computing, this book is intended to be concise and to the point. This makes it useful in practical context of reading journal articles, performing research calculations or problems in graduate courses in physics and engineering. It is designed to provide ready access to essential information on quantum information processing and communication, such as definitions, protocols and algorithms. Quantum information science is a rapidly expanding area of technology and research containing a diverse spectrum of mathematical tools rarely found in clear and concise form. This book brings together this information from its various sources. It allows researchers and students in a broad range of areas to have this vital material directly at hand when needed. This is made possible by a concise and thorough format.

Autorentext

Dr. Jaeger is a professor at Boston University, where he earned his Ph.D. in Physics with Abner Shimony in 1995. He has written over 25 journal articles, holds 2 US patents in quantum computing and has authored 2 book chapters. He has been a participant in then DARPA Quantum Network Testbed Project since 2001. Dr. Jaeger is a member of the Quantum Imaging Lab.

Inhalt

Foreword.- Section 1 Qubits: Quantum state purity.- The representation of qubits.- Stokes parameters.- Single-qubit gates.- The double-slit experiment.- The Mach-Zehnder interferometer.- Multiple qubits.- Section 2 Measurements and quantum operations: The von Neumann classification of processes.- The Pauli classification of measurements.- Maximal measurements and expectation values.- The Lueders rule and non-selective measurements.- Reduced statistical operators.- General operations.- Positive operator valued measures.- Section 3 Quantum non-locality and interferometry: Hidden variables and state completeness.- Von Neumann's 'no-go' theorem.- The Einstein-Podolsky-Rosen argument.- Gleason's theorem.- Bell inequalities.- Interferometric complementarity.- The Franson interferometer.- Two-qubit quantum gates.- Section 4 Classical information and communication: Communication channels.- Shannon entropy.- Renyi entropy.- Coding.- Error correction.- Data compression.- Communication complexity.- Section 5 Quantum information: Quantum entropy.- Quantum relative and conditional entropies.- Quantum mutual information.- Coherent information.- Quantum Renyi and Tsallis entropies.- Section 6 Quantum entanglement: Basic definitions.- The Schmidt decomposition.- Special bases and decompositions.- Stokes parameters and entanglement.- Partial transpose and reduction criteria.- The 'fundamental postulate'.- Entanglement monotones.- Distillation and bound entanglement.- Entanglement and majorization.- Concurrence.- Entanglement witnesses.- Entanglement as a resource.- The thermodynamic analogy.- Information and the foundations of physics.- The geometry of entanglement.- Creating entangled states of light.- Section 7 Entangled multipartite systems.- Stokes and correlation tensors.- N-tangle.- Generalized Schmidt decomposition.- Lorentz-group isometries.- Entanglement classes.- Algebraic invariants of multipartite systems.- Three-qubit states and residual tangle.- Three-qubit quantum logic gates.- States of higher qubit number.- Section 8 Quantum state and process estimation.- Quantum state tomography.- Quantum process tomography.- Direct estimation methods.- Section 9 Quantum communication: Quantum channels.- Channel capacities.- Holevo's theorem.- Discrimination of quantum states.- The no-cloning theorem.- Basic quantum channels.- The GHJW theorem.- Quantum dense coding.- Quantum teleportation.- Entanglement swapping.- Entanglement purification.- Quantum data compression.- Quantum communication complexity.- Section 10 Quantum decoherence and its mitigation: Quantum decoherence.- Decoherence and mixtures.- Decoherence-free subspaces.- Quantum coding, error detection and correction.- The 9-qubit Shor code.- Stabilizer codes.- Concatenation of quantum codes.- Section 11 Quantum broadcasting, copying and deleting: Quantum broadcasting.- Quantum copying.- Quantum deleting.- Landauer's principle.- Section 12 Quantum key distribution: Cryptography.- QKD systems.- The BB84 (four-state) protocol.- The E91 (Ekert) protocol.- The B92 (two-state) protocol.- The 6-state protocol.- Eavesdropping.- Security proofs.- Section 13 Classical and quantum computing: Classical computing.- Deterministic Turing machines.- Probabilistic Turing machines.- Multi-tape Turing machines . 13.5 Quantum Turing machines.- Quantum computational complexity.- Fault-tolerant quantum computing.- The KLM proposal.- Section 14 Quantum algorithms: The Deutsch-Jozsa algorithm.- The Grover search algorithm.- The Shor factoring algorithm.- The Simon algorithm.- Appendix A Mathematical elements: Boolean algebra and Galois fields.- Random variables.- Hilbert space.- The standard quantum formalism.- Dirac notation.- Groups o