Quantum Communication, Quantum Networks, and Quantum Sensing

✍ Scribed by Ivan Djordjevic

• Publisher: Academic Press
• Year: 2022
• Tongue: English
• Leaves: 624
• Edition: 1
• Category: Library

✦ Synopsis

Quantum Communication, Quantum Networks, and Quantum Sensing represents a self-contained introduction to quantum communication, quantum error-correction, quantum networks, and quantum sensing. It starts with basic concepts from classical detection theory, information theory, and channel coding fundamentals before continuing with basic principles of quantum mechanics including state vectors, operators, density operators, measurements, and dynamics of a quantum system. It continues with fundamental principles of quantum information processing, basic quantum gates, no-cloning and theorem on indistinguishability of arbitrary quantum states. The book then focuses on quantum information theory, quantum detection and Gaussian quantum information theories, and quantum key distribution (QKD). The book then covers quantum error correction codes (QECCs) before introducing quantum networks. The book concludes with quantum sensing and quantum radars, quantum machine learning and fault-tolerant quantum error correction concepts.

✦ Table of Contents

Front Cover
Quantum Communication, Quantum Networks, and Quantum Sensing
Quantum Communication, Quantum Networks, and Quantum Sensing
Copyright
Contents
Preface
1 . Basics of quantum information, quantum communication, quantum sensing, and quantum networking
1.0 Overview
1.1 Photon polarization
1.2 The concept of qubit
1.3 Quantum gates and quantum information processing
1.4 Quantum teleportation
1.5 Quantum error correction concepts
1.6 Quantum sensing
1.7 Quantum key distribution
1.8 Quantum networking
1.9 Organization of the book
References
2 . Information theory, error correction, and detection theory
2.1 Classical information theory fundamentals
2.1.1 Entropy, conditional entropy, relative entropy, and mutual information
2.1.2 Source coding and data compaction
2.1.2.1 Huffman coding
2.1.2.2 Ziv–Lempel algorithm
2.1.3 Mutual information, channel capacity, channel coding theorem, and information capacity theorem
2.1.3.1 Mutual information and information capacity
2.1.3.2 Channel coding theorem
2.1.3.3 Capacity of continuous channels
2.2 Channel coding preliminaries
2.3 Linear block codes
2.3.1 Generator matrix for linear block code
2.3.2 Parity-check matrix for linear block code
2.3.3 Distance properties of linear block codes
2.3.4 Coding gain
2.3.5 Syndrome decoding and standard array
2.3.6 Important coding bounds
2.4 Cyclic codes
2.5 Bose–Chaudhuri–Hocquenghem codes
2.5.1 Galois fields
2.5.2 The structure and encoding of Bose–Chaudhuri–Hocquenghem codes
2.5.3 Decoding of Bose–Chaudhuri–Hocquenghem codes
2.6 Reed–Solomon, concatenated, and product codes
2.7 Detection and estimation theory fundamentals
2.7.1 Geometric representation of received signals
2.7.2 Optimum and log-likelihood ratio receivers
2.7.3 Estimation theory fundamentals
2.8 Concluding remarks
References
Further reading
3 - Quantum information processing fundamentals
3.1 Quantum information processing features
3.2 State vectors, operators, projection operators, and density operators
3.2.1 State vectors and operators
3.2.2 Projection operators
3.2.3 Photon, spin-1/2 systems, and Hadamard gate
3.2.4 Density operators
3.3 Measurements, uncertainty relations, and dynamics of quantum systems
3.3.1 Measurements and generalized measurements
3.3.2 Uncertainty principle
3.3.3 Time evolution—Schrödinger equation
3.4 Superposition principle, quantum parallelism, and quantum information processing basics
3.5 No-cloning theorem
3.6 Distinguishing quantum states
3.7 Quantum entanglement
3.8 Operator-sum representation
3.9 Decoherence effects, depolarization, and amplitude damping channel models
3.10 Summary
References
Further reading
4 - Quantum information theory fundamentals
4.1 Introductory remarks
4.2 Von Neumann entropy
4.2.1 Composite systems
4.3 Holevo information, accessible information, and Holevo bound
4.4 Data compression and Schumacher's noiseless quantum coding theorem
4.4.1 Shannon's noiseless source coding theorem
4.4.2 Schumacher's noiseless quantum source coding theorem
4.5 Quantum channels
4.6 Quantum channel coding and Holevo–Schumacher–Westmoreland theorem
4.6.1 Classical error correction and Shannon's channel coding theorem
4.6.2 Quantum error correction and Holevo–Schumacher–Westmoreland theorem
4.7 Summary
References
5 - Quantum detection and quantum communication
5.1 Density operators (revisited)
5.2 Quantum detection theory fundamentals
5.3 Binary quantum detection
5.3.1 Quantum binary decision for pure states
5.4 Coherent states, quadrature operators, and uncertainty relations
5.5 Binary quantum optical communication in the absence of background radiation
5.5.1 Classical photon-counting receiver
5.5.2 Quantum photon-counting receiver
5.5.3 Optimum quantum detection for on–off keying
5.5.4 Optimum quantum detection for binary phase-shift keying
5.5.5 Near-optimum quantum detection for binary phase-shift keying (Kennedy receiver)
5.5.6 Dolinar receiver
5.6 Field coherent states, P-representation, and noise representation
5.6.1 The field coherent states and P-representation
5.6.2 Noise representation
5.7 Binary quantum detection in the presence of noise
5.8 Gaussian states, transformation, and channels, squeezed states, and Gaussian state detection
5.8.1 Gaussian and squeezed states
5.8.2 Gaussian transformations, Gaussian channels, and squeezed states
5.8.3 Thermal decomposition of Gaussian states and von Neumann entropy
5.8.4 Covariance matrices of two-mode Gaussian states
5.8.5 Gaussian state detection
5.8.5.1 Homodyne detection
5.8.5.2 Heterodyne detection
5.8.5.3 Partial measurements
5.8.6 The covariance matrices of multimode Gaussian systems and lossy transmission channel
5.9 Generation of quantum states
5.10 Multilevel quantum optical communication
5.10.1 The square root measurement-based quantum decision
5.10.2 Geometrically uniform symmetry constellations and M-ary phase-shift keying
5.10.3 Multilevel quantum optical communication in the presence of noise
5.11 Summary
References
6 - Quantum key distribution
6.1 Cryptography basics
6.2 Quantum key distribution basics
6.3 No-cloning theorem and distinguishing quantum states
6.4 Discrete variable quantum key distribution protocols
6.4.1 BB84 protocols
6.4.2 B92 protocol
6.4.3 Ekert (E91) and Einstein–Podolsky–Rosen protocols
6.4.4 Time-phase encoding
6.5 Quantum key distribution security
6.5.1 Independent (individual) or incoherent attacks
6.5.2 Collective attacks
6.5.3 Quantum hacking attacks and side-channel attacks
6.5.4 Security of BB84 protocol
6.6 Decoy-state protocols
6.7 Measurement-device-independent quantum key distribution protocols
6.7.1 Photonic bell state measurements
6.7.2 Description of measurement-device-independent quantum key distribution protocol
6.7.3 Time-phase-encoding-based measurement-device-independent quantum key distribution protocol
6.7.4 The secrecy fraction of measurement-device-independent quantum key distribution protocols
6.8 Twin-field quantum key distribution protocols
6.9 Information reconciliation and privacy amplification
6.9.1 Information reconciliation
6.9.2 Privacy amplification
6.10 Continuous variable quantum key distribution
6.10.1 Homodyne and heterodyne detection schemes
6.10.2 Squeezed state-based protocols
6.10.3 Coherent state-based continuous-variable quantum key distribution protocols
6.10.4 Secret key rate of continuous-variable quantum key distribution with Gaussian modulation under collective attacks
6.10.5 Reverse reconciliation results for Gaussian modulation-based continuous-variable quantum key distribution
6.11 Summary
References
Further reading
7 - Quantum error correction fundamentals
7.1 Pauli operators (revisited)
7.2 Quantum error correction concepts
7.2.1 Three-qubit flip code
7.2.2 Three-qubit phase flip code
7.2.3 Shor's nine-qubit code
7.2.4 Stabilizer code concepts
7.2.5 Relationship between quantum and classical codes
7.2.6 Quantum cyclic codes
7.2.7 Calderbank–Shor–Steane codes
7.2.8 Quantum codes over GF(4)
7.3 Quantum error correction
7.3.1 Redundancy and quantum error correction
7.3.2 Stabilizer group S
7.3.3 Quantum-check matrix and syndrome equation
7.3.4 Necessary and sufficient conditions for quantum error correction coding
7.3.5 A quantum stabilizer code for phase-flip channel (revisited)
7.3.6 Distance properties of quantum error correction codes
7.3.7 Calderbank–Shor–Steane codes (revisited)
7.3.8 Encoding and decoding circuits of quantum stabilizer codes
7.4 Important quantum coding bounds
7.4.1 Quantum Hamming bound
7.4.2 Quantum Gilbert–Varshamov bound
7.4.3 Quantum Singleton (Knill–Laflamme) bound [18]
7.4.4 Quantum weight enumerators and quantum MacWilliams identity
7.5 Quantum operations (superoperators) and quantum channel models
7.5.1 Operator-sum representation
7.5.2 Depolarizing channel
7.5.3 Amplitude damping channel
7.5.4 Generalized amplitude damping channel
7.6 Summary
References
8 - Quantum stabilizer codes and beyond
8.1 Stabilizer codes
8.2 Encoded operators
8.3 Finite geometry representation
8.4 Standard form of stabilizer codes
8.5 Efficient encoding and decoding
8.5.1 Efficient encoding
8.5.2 Efficient decoding
8.6 Nonbinary stabilizer codes
8.7 Subsystem codes
8.8 Topological codes
8.9 Surface codes
8.10 Entanglement-assisted quantum codes
8.10.1 Principles of entanglement-assisted quantum error correction
8.10.2 Entanglement-assisted canonical quantum codes
8.10.3 General entanglement-assisted quantum codes
8.10.4 Entanglement-assisted quantum error correction codes derived from classical quaternary and binary codes
8.11 Summary
References
Further reading
9 - Quantum low-density parity-check codes
9.1 Classical low-density parity-check codes
9.1.1 Large-girth quasi-cyclic binary low-density parity-check codes
9.1.2 Decoding of binary low-density parity-check codes
9.1.3 Bit error rate performance of binary low-density parity-check codes
9.1.4 Nonbinary low-density parity-check codes
9.1.5 Low-density parity-check code design
9.1.5.1 Gallager codes
9.1.5.2 Tanner codes and generalized low-density parity-check codes
9.1.5.3 MacKay codes
9.2 Dual-containing quantum low-density parity-check codes
9.3 Entanglement-assisted quantum low-density parity-check codes
9.4 Iterative decoding of quantum low-density parity-check codes
9.5 Spatially coupled quantum low-density parity-check codes
9.6 Summary
References
10 - Quantum networking
10.1 Quantum communications networks and the quantum Internet
10.2 Quantum teleportation and quantum relay
10.3 Entanglement distribution
10.3.1 Entanglement swapping and Bell state measurements
10.3.2 Hong–Ou–Mendel effect
10.3.3 Continuous variable quantum teleportation
10.3.4 Quantum network coding
10.4 Engineering entangled states and hybrid continuous-variable–discrete-variable quantum networks
10.4.1 Hybrid continuous-variable–discrete-variable quantum networks
10.4.2 Photon addition and photon subtraction modules
10.4.3 Generation of hybrid discrete-variable–continuous-variable entangled states
10.4.4 Hybrid continuous-variable–discrete-variable state teleportation and entanglement swapping through entangling measurements
10.4.5 Generation of entangled macroscopic light states
10.4.6 Noiseless amplification
10.5 Cluster state-based quantum networking
10.5.1 Cluster states and cluster state processing
10.5.2 Cluster state-based quantum networks
10.6 Surface code-based and quantum low-density parity-check code-based quantum networking
10.7 Entanglement-assisted communication and networking
10.7.1 Entanglement-assisted communication networks
10.7.2 Nonlinear receivers for entanglement-assisted communication systems
10.7.3 Entanglement-assisted communication with optical phase conjugation on the transmitter side
10.8 Summary
References
Further reading
11 . Quantum sensing and quantum radars
11.1 Quantum phase estimation
11.1.1 Quantum interferometry
11.1.2 Supersensitive regime and Heisenberg limit
11.2 Quantum Fisher information and quantum Cramér–Rao bound
11.2.1 Cramér–Rao bound
11.2.2 Quantum Cramér–Rao bound
11.3 Distributed quantum sensing
11.3.1 Distributed quantum sensing of in-phase displacements
11.3.2 General distributed quantum sensing of in-phase displacements
11.4 Quantum radars
11.4.1 Interferometric quantum radars
11.4.2 Quantum illumination-based quantum radars
11.4.3 Entanglement-assisted quantum radars
11.4.4 Quantum radar equation
11.5 Summary
References
12 . Quantum machine learning
12.1 Machine learning fundamentals
12.1.1 Machine learning basics
12.1.2 Principal component analysis
12.1.3 Support vector machines
12.1.3.1 Soft margin
12.1.3.2 The kernel method
12.1.4 Clustering
12.1.4.1 K-means clustering
12.1.4.2 Cluster quality
12.1.4.3 Expectation-maximization clustering
12.1.4.4 K-nearest neighbors algorithm
12.1.5 Boosting
12.1.6 Regression analysis
12.1.7 Neural networks
12.1.7.1 Perceptron and activation functions
12.1.7.2 Feedforward networks
12.2 The Ising model, adiabatic quantum computing, and quantum annealing
12.2.1 The Ising model
12.2.2 Adiabatic quantum computing
12.2.3 Quantum annealing
12.3 Quantum approximate optimization algorithm and variational quantum eigensolver
12.4 Quantum boosting
12.5 Quantum random access memory
12.6 Quantum matrix inversion
12.7 Quantum principal component analysis
12.8 Quantum optimization-based clustering
12.9 Grover algorithm-based global quantum optimization
12.10 Quantum K-means
12.10.1 Scalar product calculation
12.10.2 Quantum distance calculation
12.10.3 Grover algorithm-based K-means
12.11 Quantum support vector machines
12.12 Quantum neural networks
12.12.1 Feedforward quantum neural networks
12.12.2 Quantum perceptron
12.12.3 Quantum convolutional neural networks
12.13 Summary
References
Further reading
13 - Fault-tolerant quantum error correction
13.1 Fault-tolerance basics
13.2 Fault-tolerant quantum information processing concepts
13.2.1 Fault-tolerant Pauli gates
13.2.2 Fault-tolerant Hadamard gate
13.2.3 Fault-tolerant phase gate (P)
13.2.4 Fault-tolerant CNOT gate
13.2.5 Gate fault-tolerant π/8 (T) gate
13.2.6 Fault-tolerant measurement
13.2.7 Fault-tolerant state preparation
13.2.8 Fault-tolerant measurement of stabilizer generators
13.3 Fault-tolerant quantum error correction
13.3.1 Fault-tolerant syndrome extraction
13.3.2 Fault-tolerant encoding operations
13.3.3 Measurement protocol
13.3.4 Fault-tolerant stabilizer codes
13.3.5 The [5,1,3] fault-tolerant stabilizer code
13.4 Summary
References
Further reading
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Z
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