| Preface |
|
vii | |
|
1 Quantum Information Theory, A Selection of Matrix Inequalities |
|
|
1 | (4) |
|
1.1 Monotonicity of Quantum Relative Renyi Entropy |
|
|
1 | (2) |
|
|
|
3 | (2) |
|
2 Stochastic Filtering Theory Applied to Electromagnetic Fields and Strings |
|
|
5 | (8) |
|
2.1 M. Tech Dissertation Topics |
|
|
5 | (1) |
|
2.2 Estimating the Time Varying Permittivity and Permeability of a Region of Space Using Nonlinear Stochastic Filtering Theory |
|
|
5 | (1) |
|
2.3 Estimating the Time Varying Permittivity and Permeability of a Region of Space Using Nonlinear Stochastic Filtering Theory |
|
|
6 | (6) |
|
2.4 Study Project: Reduction of Supersymmetry Breaking by Feedback |
|
|
12 | (1) |
|
3 Wigner-distributions in Quantum Mechanics |
|
|
13 | (14) |
|
3.1 Quantum Fokker-Planck Equation in theWigner Domain |
|
|
13 | (4) |
|
3.2 The Noiseless Quantum Fokker-Planck Equation or Equivalently, the Liouville-Schrodinger-Von-Neumann-equation in the Wigner Domain |
|
|
17 | (2) |
|
3.3 Construction of the Quantum Fokker-Planck Equation for a Specific Choice of the Lindblad Operator |
|
|
19 | (2) |
|
3.4 Problems in Quantum Corrections to Classical Theories in Probability Theory and in Mechanics with Other Specific Choices of the Lindblad Operator |
|
|
21 | (1) |
|
3.5 Belavkin filter for the Wigner Distribution Function |
|
|
22 | (4) |
|
3.6 Superstring Coupled to Gravitino Ensures Local Supersymmetry |
|
|
26 | (1) |
|
4 Undergraduate and Postgraduate Courses in Electronics, Communication and Signal Processing |
|
|
27 | (2) |
|
5 Quantization of Classical Field Theories, Examples |
|
|
29 | (18) |
|
5.1 Quantization of Fluid Dynamics in a Curved Space-time Background Using Lagrange Multiplier Functions |
|
|
29 | (2) |
|
5.2 D-Dimensional Harmonic Oscillator with Electric Field Forcing |
|
|
31 | (2) |
|
5.3 A Problem: Design a Quantum Neural Network Based on Matching the Diagonal Slice of the Density Operator to a Given Probability Density Function |
|
|
33 | (1) |
|
5.4 Quantum Filtering for the Gravitational Field Interacting with the Electromagnetic Field |
|
|
33 | (3) |
|
5.5 Quantum Filtering for the Gravitational Field Interacting with the Electromagnetic Field |
|
|
36 | (5) |
|
5.6 Harmonic Oscillator with Time Varying Electric Field and Lindblad Noise with Lindblad Operators Being Linear in the Creation and Annihilation Operators, Transforms a Gaussian State into Another After Time |
|
|
41 | (2) |
|
5.7 Quantum Neural Network Using a Single Harmonic Oscillator Perturbed by an Electric Field |
|
|
43 | (4) |
|
6 Statistical Signal Processing |
|
|
47 | (20) |
|
6.1 Statistical Signal Processing: Long Test |
|
|
47 | (3) |
|
|
|
50 | (2) |
|
6.3 Lie Brackets in Quantum Mechanics in Terms of the Wigner Transform of Observables |
|
|
52 | (2) |
|
6.4 Simulation of a Class of Markov Processes in Continuous and Discrete Time with Applications to Solving PartiaLDifferential Equations |
|
|
54 | (1) |
|
6.5 Gravitational Radiation |
|
|
54 | (8) |
|
6.6 Measuring the Gravitational Radiation Using Quantum Mechanical Receivers |
|
|
62 | (5) |
|
7 Some More Concepts and Results in Quantum Information Theory |
|
|
67 | (14) |
|
7.1 Fidelity Between Two States ρ, σ |
|
|
67 | (1) |
|
7.2 An Identity Regarding Fidelity |
|
|
68 | (1) |
|
7.3 Adaptive Probability Density Tracking Using the Quantum Master Equation |
|
|
69 | (1) |
|
7.4 Quantum Neural Networks Based on Superstring Theory |
|
|
70 | (3) |
|
7.5 Designing a Quantum Neural Network for Tracking a Multivariate pdf Based on Perturbing a Multidimensional Harmonic Oscillator Hamiltonian by an An-harmonic Potential |
|
|
73 | (3) |
|
7.6 Applied Linear Algebra |
|
|
76 | (5) |
|
8 Quantum Field Theory, Quantum Statistics, Gravity, Stochastic Fields and Information |
|
|
81 | (28) |
|
8.1 Rate Distortion Theory for Ergodic Sources |
|
|
81 | (5) |
|
|
|
86 | (1) |
|
8.3 Simulation of Time Varying Joint Probability |
|
|
87 | (2) |
|
8.4 An application of the Radiatively Corrected Propagator to Quantum Neural Network Theory Densities Using Yang-Mills Gauge Theories |
|
|
89 | (2) |
|
8.5 An Experiment Involving the Measurement of Newton's Gravitational Constant G |
|
|
91 | (1) |
|
8.6 Extending the Fluctuation-Dissipation Theorem |
|
|
92 | (1) |
|
8.7 A discrete Poisson Collision Approach to Brownian Motion |
|
|
92 | (2) |
|
8.8 The Born-Oppenheimer Program |
|
|
94 | (2) |
|
8.9 The Superposition Principle for Wave Functions of the Curved Space-time Metric Field Could Lead to Contradictions and what are the Fundamental Difficulties in Developing a Background Independent Theory of Quantum Gravity |
|
|
96 | (1) |
|
8.10 Attempts to Detect Gravitational Waves from Rotating Pulsars and Sudden Burst of a Star Using Crystal Detectors |
|
|
96 | (1) |
|
8.11 Sketch of the Proof of Shannon's Coding Theorems |
|
|
97 | (2) |
|
8.12 The Notion of a Field Operator or Rather an Operator Valued Field |
|
|
99 | (3) |
|
8.13 Group Theoretic Pattern Recognition |
|
|
102 | (2) |
|
8.14 Controlling the Probability Distribution in Functional Space of the Klein-Gordon Field Using a Field Dependent Potential |
|
|
104 | (1) |
|
8.15 Quantum Processing of Classical Image Fields Using a Classical Neural Network |
|
|
105 | (1) |
|
8.16 Entropy and Supersymmetry |
|
|
105 | (4) |
|
9 Problems in Information Theory |
|
|
109 | (44) |
|
9.1 Problems in Quantum Neural Networks |
|
|
139 | (2) |
|
9.2 MATLAB Simulation Exercises in Statistical Signal Processing |
|
|
141 | (2) |
|
9.3 Problems in Information Theory |
|
|
143 | (2) |
|
9.4 Problems in Quantum Neural Networks |
|
|
145 | (1) |
|
9.5 Quantum Gaussian States and Their Transformations |
|
|
146 | (7) |
|
10 Lecture Plan for Information Theory, Sanov's Theorem, Quantum Hypothesis Testing and State Transmission, Quantum Entanglement, Quantum Security |
|
|
153 | (18) |
|
|
|
153 | (2) |
|
10.2 A problem in Information Theory |
|
|
155 | (2) |
|
10.3 Types and Sanov's Theorem |
|
|
157 | (2) |
|
10.4 Quantum Stein's Theorem |
|
|
159 | (2) |
|
10.5 Problems in Statistical Image Processing |
|
|
161 | (3) |
|
10.6 A Remark on Quantum State Transmission |
|
|
164 | (1) |
|
10.7 An Example of a Cq Channel |
|
|
165 | (2) |
|
10.8 Quantum State Transformation Using Entangled States |
|
|
167 | (1) |
|
10.9 Generation of Entangled States from Tensor Product States |
|
|
168 | (1) |
|
10.10 Security in Quantum Communication from Eavesdroppers |
|
|
168 | (1) |
|
10.11 Abstract on Internet of Things in Electromagnetics and Quantum Mechanics |
|
|
169 | (2) |
|
11 More Problems in Classical and Quantum Information Theory |
|
|
171 | (18) |
|
|
|
171 | (12) |
|
11.2 Examples of Cq data Transmission |
|
|
183 | (6) |
|
12 Information Transmission and Compression with Distortion, Ergodic Theorem, Quantum Blackhole Physics |
|
|
189 | (38) |
|
12.1 Examples of Cq data Transmission |
|
|
189 | (2) |
|
12.2 The Shannon-Mcmillan-Breiman Theorem |
|
|
191 | (2) |
|
12.3 Entropy Pumped by the Bath into a Quantum System as Measured by An Observer Making Noisy Non-demolition Measurements |
|
|
193 | (3) |
|
12.4 Prove the Joint Convexity of the Relative Entropy Between two Probability Distributions Along the Following Steps |
|
|
196 | (1) |
|
12.5 Quantum Blackhole Physics and the Amount of Information Pumped by the Quantum Gravitating Blackhole Into a System of Other Elementary Particles |
|
|
197 | (1) |
|
12.6 Direct Part of the Capacity Theorem for Relay Channels |
|
|
198 | (4) |
|
12.7 An Entropy Inequality |
|
|
202 | (1) |
|
12.8 Entropy Pumped by a Random Electromagnetic Field and Bath Noise Into an Electron |
|
|
202 | (1) |
|
12.9 Some Problems in the Detection and Transmission of Electromagnetic Signals and Image Fields Using Quantum Communication Techniques |
|
|
203 | (5) |
|
12.10 The Degraded Broadcast Channel |
|
|
208 | (2) |
|
12.11 Rate Distortion with Side Information |
|
|
210 | (3) |
|
12.12 Proof of the Stein Theorem in Classical Hypothesis Testing |
|
|
213 | (2) |
|
12.3 Source Coding with Side Information |
|
|
215 | (2) |
|
12.14 Some Problems on Random Segmentation of Image Fields |
|
|
217 | (4) |
|
|
|
221 | (3) |
|
12.16 Some Control Problems Involving the Theory of Large Deviations |
|
|
224 | (3) |
|
13 Examination Problems in Classical Information Theory |
|
|
227 | |
|
13.1 Converse Part of the Achievability Result for a Multiterminal Network |
|
|
236 | (2) |
|
13.2 More Examination Problems in Information Theory |
|
|
238 | |
More info about Taylor & Francis e-books