Quantum Information: An Overview

Quantum information science is a rapidly expanding area of technology. This book offers an overview of this field for practitioners and students of quantum physics and information science. It provides information on quantum information processing and communication, such as definitions, protocols and algorithms.

This book is a comprehensive yet concise overview of quantum information science, which is a rapidly developing area of interdisciplinary investigation that now plays a significant role in physics, information technology and engineering. The most well-known applications of quantum information science are quantum key distribution and quantum computation. This book is a handy reference for practitioners and students covering foundational issues as well as these and other applications. It contains more than 25 illustrations that encapsulate essential ideas and fundamental constructs. It contains a Foreword by Prof. Tommaso Toffoli.

Foreword		vii
Preface		xi
Acknowledgments		xiii
Qubits		1	(28)
Quantum state purity		5	(3)
The representation of qubits		8	(3)
Stokes parameters		11	(3)
Single-qubit gates		14	(4)
The double-slit experiment		18	(5)
The Mach-Zehnder interferometer		23	(2)
Quantum coherence and information processing		25	(4)
Measurements and quantum operations		29	(16)
The von Neumann classification of processes		32	(2)
The Pauli classification of measurements		34	(1)
Expectation values and the von Neumann projection		35	(2)
The Luders rule		37	(1)
Reduced statistical operators		38	(1)
General quantum operations		39	(2)
Positive-operator-valued measures		41	(4)
Quantum nonlocality and interferometry		45	(22)
Hidden variables and state completeness		46	(2)
Von Neumann's ``no-go'' theorem		48	(1)
The Einstein--Podolsky--Rosen argument		49	(2)
Gleason's theorem		51	(1)
Bell inequalities		52	(5)
Interferometric complementarity		57	(4)
The Franson interferometer		61	(2)
Two-qubit quantum gates		63	(4)
Classical information and communication		67	(14)
Communication channels		68	(2)
Shannon entropy		70	(4)
Renyi entropy		74	(1)
Coding		74	(3)
Error correction		77	(1)
Data compression		78	(1)
Communication complexity		79	(2)
Quantum information		81	(10)
Quantum entropy		82	(2)
Quantum relative and conditional entropies		84	(1)
Quantum mutual information		85	(1)
Fidelity and coherent information		86	(2)
Quantum Renyi and Tsallis entropies		88	(3)
Quantum entanglement		91	(30)
Basic definitions		92	(2)
The Schmidt decomposition		94	(1)
Special bases and decompositions		95	(3)
Stokes parameters and entanglement		98	(1)
Partial transpose and reduction criteria		99	(2)
The ``fundamental postulate''		101	(1)
Entanglement monotones		102	(2)
Distillation and bound entanglement		104	(1)
Entanglement and majorization		105	(1)
Concurrence		106	(1)
Entanglement witnesses		107	(1)
Entanglement as a resource		108	(1)
The thermodynamic analogy		109	(3)
Information and the foundations of physics		112	(2)
The geometry of entanglement		114	(1)
Creating entangled photons		115	(6)
Entangled multipartite systems		121	(18)
Stokes and correlation tensors		124	(2)
N-tangle		126	(1)
Generalized Schmidt decomposition		127	(1)
Lorentz-group isometries		127	(2)
Entanglement classes		129	(2)
Algebraic invariants of multipartite systems		131	(2)
Three-qubit states and residual tangle		133	(2)
Three-qubit quantum logic gates		135	(1)
States of higher qubit number		136	(3)
Quantum state and process estimation		139	(8)
Quantum state tomography		140	(3)
Quantum process tomography		143	(1)
Direct estimation methods		144	(3)
Quantum communication		147	(24)
Quantum channels		148	(1)
Quantum channel capacities		149	(2)
Holevo's theorem		151	(2)
Discrimination of quantum states		153	(3)
The no-cloning theorem		156	(1)
Basic quantum channels		157	(2)
The GHJW theorem		159	(1)
Quantum dense coding		160	(2)
Quantum teleportation		162	(2)
Entanglement ``swapping''		164	(1)
Entanglement ``purification''		165	(2)
Quantum data compression		167	(2)
Quantum communication complexity		169	(2)
Quantum decoherence and its mitigation		171	(14)
Quantum decoherence		172	(1)
Decoherence and mixtures		173	(1)
Decoherence-free subspaces		174	(1)
Quantum coding, error detection, and correction		175	(4)
The nine-qubit Shor code		179	(2)
Stabilizer codes		181	(2)
Concatenation of quantum codes		183	(2)
Quantum broadcasting, copying, and deleting		185	(6)
Quantum broadcasting		185	(1)
Quantum copying		186	(3)
Quantum deleting		189	(1)
Landauer's principle		190	(1)
Quantum key distribution		191	(12)
Cryptography and cryptosystems		191	(2)
QKD systems		193	(2)
The BB84 (four-state) protocol		195	(2)
The E91 (Ekert) protocol		197	(1)
The B92 (two-state) protocol		198	(1)
The six-state protocol		199	(1)
Eavesdropping		199	(2)
Security proofs		201	(2)
Classical and quantum computing		203	(16)
Classical computing and computational complexity		204	(2)
Deterministic Turing machines		206	(1)
Probabilistic Turing machines		207	(1)
Multi-tape Turing machines		208	(1)
Quantum Turing machines		209	(2)
Quantum computational complexity		211	(3)
Fault-tolerant quantum computing		214	(1)
Linear optical quantum computation		215	(4)
Quantum algorithms		219	(12)
The Deutsch--Jozsa algorithm		220	(1)
The Grover search algorithm		221	(3)
The Shor factoring algorithm		224	(5)
The Simon algorithm		229	(2)
A. Mathematical elements		231	(14)
Boolean algebra and Galois fields		231	(1)
Random variables		232	(1)
Vector Spaces and Hilbert space		233	(4)
The standard quantum formalism		237	(1)
The Dirac notation		237	(2)
Groups of transformations		239	(1)
Probability, lattices, and posets		240	(2)
Projectors, correlations, and the Kochen--Specker theorem		242	(1)
Traditional quantum logic		243	(2)
B. The quantum postulates		245	(4)
The standard postulates		245	(2)
The Heisenberg--Robertson uncertainty relation		247	(1)
Liouville space and open quantum systems		248	(1)
References		249	(22)
Index		271

Dr. Jaeger is a professor at Boston University, where he earned his Ph.D. in Physics with Abner Shimony in 1995. He has published in a number of areas, including quantum computing, quantum cryptography, foundations of quantum mechanics, quantum metrology, and the history and philosophy of science. He was worked in academia and industry in the United States and Europe as a research director and investigator in quantum information science and quantum metrology. As a member of the Quantum Imaging Laboratory at Boston University's Photonics Center, along with colleagues at Harvard University and BBN Technologies, he helped build the world's first practical metropolitan area quantum cryptographic network, the DARPA Quantum Network Test-bed, serving as principal quantum entanglement theorist.