Classical and quantum information theory for the physicist:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
2023
New Delhi Manakin Press |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xviii, 244 Seiten |
| ISBN: | 9781032405179 9781032405209 |
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| 245 | 1 | 0 | |a Classical and quantum information theory for the physicist |c Harish Parthasarathy, Professor, Electronics & Communication Engineering Netaji Subhas Institute of Technology (NSIT), Nwe Delhi, Delhi-110078 |
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Detailed Contents Preface vii-xiv 1. Quantum Information Theory, A Selection of Matrix Inequalities 1.1 Monotonicity of Quantum Relative Renyi Entropy 1.2 Problems 2. 1-4 I 3 Stochastic Filtering Theory Applied to Electromagnetic Fields and Strings 5-12 2.1 M.Tech Dissertation Topics 5 2.2 Estimating the Time Vaiying Permittivity and Permeability of a Region of Space Using Nonlinear Stochastic Filtering Theory 5 2.3 Estimating the Time Varying Permittivity and Permeability of a Region of Space Using Nonlinear Stochastic Filtering Theoiy 6 2.4 Study Project: Reduction of Supersymmetry Breaking by Feedback 12 3. Wigner-distributions in Quantum Mechanics 13-26 3.1 Quantum Fokker-Planck Equation in theWigner Domain 13 3.2 The Noiseless Quantum Fokker-Planck Equation or Equivalently, the Liouville-Schrodinger- Von-Neumann-equation in the Wigner Domain 17 3.3 Construction of the Quantum Fokker-Planck Equation for a Specific Choice of the Lindblad Operator 19 3.4 Problems in Quantum Corrections to Classical Theories in Probability Theory and in Mechanics with Other Specific Choices of the Lindblad Operator 21 3.5 Belavkin filter for the Wigner Distribution Function 22 3.6 Superstring Coupled to Gravitino Ensures Local Supersymmetiy 26 4. Undergraduate and Postgraduate Courses in Electronics, Communication and Signal Processing 27-28 5. Quantization of Classical Field Theories, Examples 29-46 5.1 Quantization of Fluid Dynamics in a Curved Space-time Background Using Lagrange Multiplier Functions 29 5.2 d-dimensional Harmonic Oscillator with Electric Field Forcing 31 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 vii
5.4 Quantum Filtering for the Gravitational Field Interacting with the Electromagnetic Field 33 5.5 Quantum Filtering for the Gravitational Field Interacting with the Electromagnetic Field 36 5.6 Harmonic Oscillator with Time Vajying 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 41 5.7 Quantum Neural Network Using a Single Harmonic Oscillator Perturbed by an Electric Field 43 6. Statistical Signal Processing 47-66 6.1 Statistical Signal Processing: Long Test 47 6.2 Quantum EKF 50 6.3 Lie Brackets in Quantum Mechanics in Terms of the Wigner Transform of Observables 52 6.4 Simulation of a Class of Markov Processes in Continuous and Discrete Time with Applications to Solving Partial Differential Equations 54 6.5 Gravitational Radiation 54 6.6 Measuring the Gravitational Radiation Using Quantum Mechanical Receivers 62 7. Some More Concepts and Results in Quantum Information Theory 67-80 7.1 Fidelity Between TwoStates p, σ 67 7.2 An Identity Regarding Fidelity 68 7.3 Adaptive Probability Density Tracking Using the Quantum Master Equation 69 7.4 Quantum Neural Networks Based on Superstring Theojty 70 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 7.6 Applied Linear Algebra 76 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 viii 81-108 81 86 87
8.4 An application of the Radiatively Corrected Propagator to Quantum Neural Network Theory Densities Using Yang-Mills Gauge Theories 89 8.5 An Experiment Involving the Measurement of Newton’s Gravitational Constant G 91 8.6 Extending the Fluctuation-Dissipation Theorem 92 8.7 A discrete Poisson Collision Approachto Brownian Motion 92 8.8 The Born-Oppenheimer Program 94 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 8.10 Attempts to Detect Gravitational Waves from Rotating Pulsars and Sudden Burst of a Star Using Crystal Detectors 96 8.11 Sketch of the Proof of Shannon’s Coding Theorems 97 8.12 The Notion of a Field Operator or Rather an Operator Valued Field 99 8.13 Group Theoretic Pattern Recognition 102 8.14 Controlling the Probability Distribution in Functional Space of the Klein-Gordon F ield U sing a F ield Dependent Potential 104 8.15 Quantum Processing of Classical Image Fields Using a Classical Neural Network 105 8.16 Entropy and Supersymmetry 105 9. Problems in Information Theory 109-152 9.1 Problems in Quantum Neural Networks 139 9.2 MATLAB Simulation Exercises in Statistical Signal Processing 141 9.3 Problems in Information Theory 143 9.4 Problems in Quantum Neural Networks 145 9.5 Quantum Gaussian States and Their Transformations 146 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 153-170 153 155 157 159 161 164 165 167
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 169 168 168 11. More Problems in Classical and Quantum Information Theory 171-188 11.1 Problems 171 11.2 Examples of Cq data Transmission 183 12. Information Transmission and Compression with Distortion, Ergodic Theorem, Quantum Blackhole Physics 189-226 12.1 Examples of Cq data Transmission 189 12.2 The Shannon-Mcmillan-Breiman Theorem 191 12.3 Entropy Pumped by the Bath into a Quantum System as Measured by An Observer Making Noisy N on-demolition Measurements 193 12.4 Prove the Joint Convexity of the Relative Entropy Between two Probability Distributions Along the Following Steps 196 12.5 Quantum Blackhole Physics and the Amount of Information Pumped by the Quantum Gravitating Blackhole Into a System of Other Elementary Particles 197 12.6 Direct Part of the Capacity Theorem for Relay Channels 198 12.7 An Entropy Inequality 202 12.8 Entropy Pumped by a Random Electromagnetic Field and Bath Noise Into an Electron 202 12.9 Some Problems in the Detection and Transmission of Electromagnetic Signals and Image Fields Using Quantum Communication Techniques 203 12.10 The Degraded Broadcast Channel 208 12.11 Rate Distortion with Side Information 210 12.12 Proof of the Stein Theorem in Classical Hypothesis Testing 213 12.3 Source Coding with Side Information 215 12.14 Some Problems on Random Segmentation of Image Fields 217 12.15 The Shannon Code 221 12.16 Some Control Problems
Involving the Theory of Large Deviations 224 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 x 227-244 236 238 |
| adam_txt |
Detailed Contents Preface vii-xiv 1. Quantum Information Theory, A Selection of Matrix Inequalities 1.1 Monotonicity of Quantum Relative Renyi Entropy 1.2 Problems 2. 1-4 I 3 Stochastic Filtering Theory Applied to Electromagnetic Fields and Strings 5-12 2.1 M.Tech Dissertation Topics 5 2.2 Estimating the Time Vaiying Permittivity and Permeability of a Region of Space Using Nonlinear Stochastic Filtering Theory 5 2.3 Estimating the Time Varying Permittivity and Permeability of a Region of Space Using Nonlinear Stochastic Filtering Theoiy 6 2.4 Study Project: Reduction of Supersymmetry Breaking by Feedback 12 3. Wigner-distributions in Quantum Mechanics 13-26 3.1 Quantum Fokker-Planck Equation in theWigner Domain 13 3.2 The Noiseless Quantum Fokker-Planck Equation or Equivalently, the Liouville-Schrodinger- Von-Neumann-equation in the Wigner Domain 17 3.3 Construction of the Quantum Fokker-Planck Equation for a Specific Choice of the Lindblad Operator 19 3.4 Problems in Quantum Corrections to Classical Theories in Probability Theory and in Mechanics with Other Specific Choices of the Lindblad Operator 21 3.5 Belavkin filter for the Wigner Distribution Function 22 3.6 Superstring Coupled to Gravitino Ensures Local Supersymmetiy 26 4. Undergraduate and Postgraduate Courses in Electronics, Communication and Signal Processing 27-28 5. Quantization of Classical Field Theories, Examples 29-46 5.1 Quantization of Fluid Dynamics in a Curved Space-time Background Using Lagrange Multiplier Functions 29 5.2 d-dimensional Harmonic Oscillator with Electric Field Forcing 31 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 vii
5.4 Quantum Filtering for the Gravitational Field Interacting with the Electromagnetic Field 33 5.5 Quantum Filtering for the Gravitational Field Interacting with the Electromagnetic Field 36 5.6 Harmonic Oscillator with Time Vajying 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 41 5.7 Quantum Neural Network Using a Single Harmonic Oscillator Perturbed by an Electric Field 43 6. Statistical Signal Processing 47-66 6.1 Statistical Signal Processing: Long Test 47 6.2 Quantum EKF 50 6.3 Lie Brackets in Quantum Mechanics in Terms of the Wigner Transform of Observables 52 6.4 Simulation of a Class of Markov Processes in Continuous and Discrete Time with Applications to Solving Partial Differential Equations 54 6.5 Gravitational Radiation 54 6.6 Measuring the Gravitational Radiation Using Quantum Mechanical Receivers 62 7. Some More Concepts and Results in Quantum Information Theory 67-80 7.1 Fidelity Between TwoStates p, σ 67 7.2 An Identity Regarding Fidelity 68 7.3 Adaptive Probability Density Tracking Using the Quantum Master Equation 69 7.4 Quantum Neural Networks Based on Superstring Theojty 70 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 7.6 Applied Linear Algebra 76 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 viii 81-108 81 86 87
8.4 An application of the Radiatively Corrected Propagator to Quantum Neural Network Theory Densities Using Yang-Mills Gauge Theories 89 8.5 An Experiment Involving the Measurement of Newton’s Gravitational Constant G 91 8.6 Extending the Fluctuation-Dissipation Theorem 92 8.7 A discrete Poisson Collision Approachto Brownian Motion 92 8.8 The Born-Oppenheimer Program 94 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 8.10 Attempts to Detect Gravitational Waves from Rotating Pulsars and Sudden Burst of a Star Using Crystal Detectors 96 8.11 Sketch of the Proof of Shannon’s Coding Theorems 97 8.12 The Notion of a Field Operator or Rather an Operator Valued Field 99 8.13 Group Theoretic Pattern Recognition 102 8.14 Controlling the Probability Distribution in Functional Space of the Klein-Gordon F ield U sing a F ield Dependent Potential 104 8.15 Quantum Processing of Classical Image Fields Using a Classical Neural Network 105 8.16 Entropy and Supersymmetry 105 9. Problems in Information Theory 109-152 9.1 Problems in Quantum Neural Networks 139 9.2 MATLAB Simulation Exercises in Statistical Signal Processing 141 9.3 Problems in Information Theory 143 9.4 Problems in Quantum Neural Networks 145 9.5 Quantum Gaussian States and Their Transformations 146 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 153-170 153 155 157 159 161 164 165 167
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 169 168 168 11. More Problems in Classical and Quantum Information Theory 171-188 11.1 Problems 171 11.2 Examples of Cq data Transmission 183 12. Information Transmission and Compression with Distortion, Ergodic Theorem, Quantum Blackhole Physics 189-226 12.1 Examples of Cq data Transmission 189 12.2 The Shannon-Mcmillan-Breiman Theorem 191 12.3 Entropy Pumped by the Bath into a Quantum System as Measured by An Observer Making Noisy N on-demolition Measurements 193 12.4 Prove the Joint Convexity of the Relative Entropy Between two Probability Distributions Along the Following Steps 196 12.5 Quantum Blackhole Physics and the Amount of Information Pumped by the Quantum Gravitating Blackhole Into a System of Other Elementary Particles 197 12.6 Direct Part of the Capacity Theorem for Relay Channels 198 12.7 An Entropy Inequality 202 12.8 Entropy Pumped by a Random Electromagnetic Field and Bath Noise Into an Electron 202 12.9 Some Problems in the Detection and Transmission of Electromagnetic Signals and Image Fields Using Quantum Communication Techniques 203 12.10 The Degraded Broadcast Channel 208 12.11 Rate Distortion with Side Information 210 12.12 Proof of the Stein Theorem in Classical Hypothesis Testing 213 12.3 Source Coding with Side Information 215 12.14 Some Problems on Random Segmentation of Image Fields 217 12.15 The Shannon Code 221 12.16 Some Control Problems
Involving the Theory of Large Deviations 224 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 x 227-244 236 238 |
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| spelling | Parthasarathy, Harish 1968- Verfasser (DE-588)1232007595 aut Classical and quantum information theory for the physicist Harish Parthasarathy, Professor, Electronics & Communication Engineering Netaji Subhas Institute of Technology (NSIT), Nwe Delhi, Delhi-110078 Boca Raton ; London ; New York CRC Press 2023 New Delhi Manakin Press ©2023 xviii, 244 Seiten txt rdacontent n rdamedia nc rdacarrier Information theory Physics Quantum theory Quanteninformation (DE-588)1211521885 gnd rswk-swf Quanteninformation (DE-588)1211521885 s DE-604 Erscheint auch als Online-Ausgabe 978-1-00-335345-4 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034254579&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Classical and quantum information theory for the physicist |
| title_auth | Classical and quantum information theory for the physicist |
| title_exact_search | Classical and quantum information theory for the physicist |
| title_exact_search_txtP | Classical and quantum information theory for the physicist |
| title_full | Classical and quantum information theory for the physicist Harish Parthasarathy, Professor, Electronics & Communication Engineering Netaji Subhas Institute of Technology (NSIT), Nwe Delhi, Delhi-110078 |
| title_fullStr | Classical and quantum information theory for the physicist Harish Parthasarathy, Professor, Electronics & Communication Engineering Netaji Subhas Institute of Technology (NSIT), Nwe Delhi, Delhi-110078 |
| title_full_unstemmed | Classical and quantum information theory for the physicist Harish Parthasarathy, Professor, Electronics & Communication Engineering Netaji Subhas Institute of Technology (NSIT), Nwe Delhi, Delhi-110078 |
| title_short | Classical and quantum information theory for the physicist |
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| topic | Information theory Physics Quantum theory Quanteninformation (DE-588)1211521885 gnd |
| topic_facet | Information theory Physics Quantum theory Quanteninformation |
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