Contents -- 1 Probability and information -- 1.1 Introduction -- 1.2 Conditional probabilities -- 1.3 Entropy and information -- 1.4 Communications theory -- Suggestions for further reading -- Exercises -- 2 Elements of quantum theory -- 2.1 Basic principles -- 2.2 Mixed states -- 2.3 Unitary operators -- 2.4 Qubits -- 2.5 Entangled states -- Suggestions for further reading -- Exercises -- 3 Quantum cryptography -- 3.1 Information security -- 3.2 Quantum communications -- 3.3 Optical polarization -- 3.4 Quantum key distribution -- Suggestions for further reading -- Exercises -- 4 Generalized measurements -- 4.1 Ideal von Neumann measurements -- 4.2 Non-ideal measurements -- 4.3 Probability operator measures -- 4.4 Optimized measurements -- 4.5 Operations -- Suggestions for further reading -- Exercises -- 5 Entanglement -- 5.1 Non-locality -- 5.2 Indirect measurements -- 5.3 Ebits and shared entanglement -- 5.4 Quantum dense coding -- 5.5 Teleportation -- Suggestions for further reading -- Exercises -- 6 Quantum information processing -- 6.1 Digital electronics -- 6.2 Quantum gates -- 6.3 Quantum circuits -- 6.4 Quantum error correction -- 6.5 Cluster states -- Suggestions for further reading -- Exercises -- 7 Quantum computation -- 7.1 Elements of computer science -- 7.2 Principles of quantum computation -- 7.3 The quantum Fourier transform -- 7.4 Shor's factoring algorithm -- 7.5 Grover's search algorithm -- 7.6 Physical requirements -- Suggestions for further reading -- Exercises -- 8 Quantum information theory -- 8.1 The von Neumann entropy -- 8.2 Composite systems -- 8.3 Quantitative state comparison -- 8.4 Measures of entanglement -- 8.5 Quantum communications theory -- Suggestions for further reading -- Exercises -- A: The equivalence of information and entropy -- B: Lagrange multipliers -- C: Stirling's approximation.

D: The Schmidt decomposition -- E: Number theory for cryptography -- E.1 Division properties -- E.2 Least common multiple and greatest common divisor -- E.3 Prime numbers -- E.4 Relatively prime integers and Euler's φ-function -- E.5 Congruences -- E.6 Primitive root modulo p -- E.7 Diffie-Hellman cryptosystem -- E.8 RSA cryptosystem -- F: Quantum copying -- G: Quantized field modes -- H: Position and momentum eigenstates -- I: Necessary conditions for a minimum-error POM -- J: Complete positivity -- K: Hardy's theorem -- L: Universal gates -- M: Nine- and five-qubit quantum codewords -- N: Computational complexity -- O: The Bernstein-Vazirani algorithm -- P: Discrete Fourier transforms -- Q: An entropy inequality -- R: Quantum relative entropy -- S: The Araki-Lieb inequality -- T: Fidelity for mixed states -- U: Entanglement of formation for two qubits -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X.