Quantum Information 1st edition by Stephen Barnett – Ebook PDF Instant Download/Delivery: 0191569920, 9780191569920
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ISBN 10: 0191569920
ISBN 13: 9780191569920
Author: Stephen Barnett
Quantum information- the subject- is a new and exciting area of science, which brings together physics, information theory, computer science and mathematics. “Quantum Information”- the book- is based on two successful lecture courses given to advanced undergraduate and beginning postgraduate students in physics. The intention is to introduce readers at this level to the fundamental, but offer rather simple, ideas behind ground-breaking developments including quantum cryptography, teleportation and quantum computing. The text is necessarily rather mathematical in style, but the mathematics nowhere allowed priority over the key physical ideas. My aim throughout was to be as complete and self- contained but to avoid, as far as possible, lengthy and formal mathematical proofs. Each of the eight chapters is followed by about forty exercise problems with which the reader can test their understanding and hone their skills. These will also provide a valuable resource to tutors and lectures.
Quantum Information 1st Table of 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
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