Classical and Quantum Information Theory for the Physicist

Cover
Half Title
Title Page
Copyright Page
Brief Contents
Table of Contents
Preface
1. Quantum Information Theory, A Selection of Matrix Inequalities
1.1 Monotonicity of Quantum Relative Renyi Entropy
1.2 Problems
2. Stochastic Filtering Theory Applied to Electromagnetic Fields and Strings
2.1 M.Tech Dissertation Topics
2.2 Estimating the Time Varying Permittivity and Permeability of a Region of Space Using Nonlinear Stochastic Filtering Theory
2.3 Estimating the Time Varying Permittivity and Permeability of a Region of Space Using Nonlinear Stochastic Filtering Theory
2.4 Study Project: Reduction of Supersymmetry Breaking by Feedback
3. Wigner-distributions in Quantum Mechanics
3.1 Quantum Fokker-Planck Equation in theWigner Domain
3.2 The Noiseless Quantum Fokker-Planck Equation or Equivalently, the Liouville-Schrodinger- Von-Neumann-equation in the Wigner Domain
3.3 Construction of the Quantum Fokker-Planck Equation for a Specific Choice of the Lindblad Operator
3.4 Problems in Quantum Corrections to Classical Theories in Probability Theory and in Mechanics with Other Specific Choices of the Lindblad Operator
3.5 Belavkin filter for the Wigner Distribution Function
3.6 Superstring Coupled to Gravitino Ensures Local Supersymmetry
4. Undergraduate and Postgraduate Courses in Electronics, Communication and Signal Processing
5. Quantization of Classical Field Theories, Examples
5.1 Quantization of Fluid Dynamics in a Curved Space-time Background Using Lagrange Multiplier Functions
5.2 d-dimensional Harmonic Oscillator with Electric Field Forcing
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
5.4 Quantum Filtering for the Gravitational Field Interacting with the Electromagnetic Field
5.5 Quantum Filtering for the Gravitational Field Interacting with the Electromagnetic Field
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 t
5.7 Quantum Neural Network Using a Single Harmonic Oscillator Perturbed by an Electric Field
6. Statistical Signal Processing
6.1 Statistical Signal Processing: Long Test
6.2 Quantum EKF
6.3 Lie Brackets in Quantum Mechanics in Terms of the Wigner Transform of Observables
6.4 Simulation of a Class of Markov Processes in Continuous and Discrete Time with Applications to Solving Partial Differential Equations
6.5 Gravitational Radiation
6.6 Measuring the Gravitational Radiation Using Quantum Mechanical Receivers
7. Some More Concepts and Results in Quantum Information Theory
7.1 Fidelity Between Two States ρ, σ
7.2 An Identity Regarding Fidelity
7.3 Adaptive Probability Density Tracking Using the Quantum Master Equation
7.4 Quantum Neural Networks Based on Superstring Theory
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
7.6 Applied Linear Algebra
8. Quantum Field Theory, Quantum Statistics, Gravity, Stochastic Fields and Information
8.1 Rate Distortion Theory for Ergodic Sources
8.2 Problems
8.3 Simulation of Time Varying Joint Probability
8.4 An application of the Radiatively Corrected Propagator to Quantum Neural Network Theory Densities Using Yang-Mills Gauge Theories
8.5 An Experiment Involving the Measurement of Newton’s Gravitational Constant G
8.6 Extending the Fluctuation-Dissipation Theorem
8.7 A discrete Poisson Collision Approach to Brownian Motion
8.8 The Born-Oppenheimer Program
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
8.10 Attempts to Detect Gravitational Waves from Rotating Pulsars and Sudden Burst of a Star Using Crystal Detectors
8.11 Sketch of the Proof of Shannon’s Coding Theorems
8.12 The Notion of a Field Operator or Rather an Operator Valued Field
8.13 Group Theoretic Pattern Recognition
8.14 Controlling the Probability Distribution in Functional Space of the Klein-Gordon Field Using a Field Dependent Potential
8.15 Quantum Processing of Classical Image Fields Using a Classical Neural Network
8.16 Entropy and Supersymmetry
9. Problems in Information Theory
9.1 Problems in Quantum Neural Networks
9.2 MATLAB Simulation Exercises in Statistical Signal Processing
9.3 Problems in Information Theory
9.4 Problems in Quantum Neural Networks
9.5 Quantum Gaussian States and Their Transformations
10. Lecture Plan for Information Theory, Sanov’s Theorem, Quantum Hypothesis Testing and State Transmission, Quantum Entanglement, Quantum Security
10.1 Lecture Plan
10.2 A problem in Information Theory
10.3 Types and Sanov’s Theorem
10.4 Quantum Stein’s Theorem
10.5 Problems in Statistical Image Processing
10.6 A Remark on Quantum State Transmission
10.7 An Example of a Cq Channel
10.8 Quantum State Transformation Using Entangled States
10.9 Generation of Entangled States from Tensor Product States
10.10 Security in Quantum Communication from Eavesdroppers
10.11 Abstract on Internet of Things in Electromagnetics and Quantum Mechanics
11. More Problems in Classical and Quantum Information Theory
11.1 Problems
11.2 Examples of Cq data Transmission
12. Information Transmission and Compression with Distortion, Ergodic Theorem, Quantum Blackhole Physics
12.1 Examples of Cq data Transmission
12.2 The Shannon-Mcmillan-Breiman Theorem
12.3 Entropy Pumped by the Bath into a Quantum System as Measured by An Observer Making Noisy Non-demolition Measurements
12.4 Prove the Joint Convexity of the Relative Entropy Between two Probability Distributions Along the Following Steps
12.5 Quantum Blackhole Physics and the Amount of Information Pumped by the Quantum Gravitating Blackhole Into a System of Other Elementary Particles
12.6 Direct Part of the Capacity Theorem for Relay Channels
12.7 An Entropy Inequality
12.8 Entropy Pumped by a Random Electromagnetic Field and Bath Noise Into an Electron
12.9 Some Problems in the Detection and Transmission of Electromagnetic Signals and Image Fields Using Quantum Communication Techniques
12.10 The Degraded Broadcast Channel
12.11 Rate Distortion with Side Information
12.12 Proof of the Stein Theorem in Classical Hypothesis Testing
12.3 Source Coding with Side Information
12.14 Some Problems on Random Segmentation of Image Fields
12.15 The Shannon Code
12.16 Some Control Problems Involving the Theory of Large Deviations
13. Examination Problems in Classical Information Theory
13.1 Converse Part of the Achievability Result for a Multiterminal Network
13.2 More Examination Problems in Information Theory