Conjugate Construction of Quantum Optics: From Foundations to Applications


Jeffrey Zheng, PhD – Professor, Yunnan University, China

Series: Physics Research and Technology
BISAC: SCI053000

This book is composed of three parts, I–III to form quantum measurement foundation on multiple variables of complex vector functions.

Four chapters in Part I establish the conjugate foundation on the conjugate complex vector system, conjugate {0,1} logic, conjugate algebra, and time measuring orders. Three chapters in Part II discuss past, current and future issues on the history of complex conjugate functions , as well as quantum entanglement paradoxes, and proposes three types of quantum entangled processes.

Facing century challenges of great quantum events (Einstein & Bohr debates, Schrodinger cats, advanced theories and experiments of quantum entanglements), conflicting/paradox facts appeared in the quantum foundation, uncertain principle, EPR and Bell inequality. Different from a series of real eigenvalue solutions based on the unit cycle of real coefficients of Hilbert spaces, this book proposes a structural framework of complex vector eigenvalue solutions based on conjugate {0,1} logic and conjugate algebra on the unit cycle of complex coefficients of conjugate spaces.

A bit unit that spreads from a qubit to a cobit satisfies a necessary and sufficient condition for complete representations of complex dynamic systems. Three measuring units, Bit, Qubit and Cobit, are consistently based on three logic frameworks, conjugate brackets/Lie Dirac brackets, and conjugate algebra/Lie Dirac algebra on conjugate foundations of quantum optics. Lie-Dirac algebra is a subset of conjugate algebra and classical quantum theory is a substructure of conjugate transformation. In conjugate construction, a consistent measuring frame for quantum optics is composed of three measuring modes as a specific application with sufficient phase spaces to fully clarify stranger quantum entanglement effects.

More than 240 prime statements are collected in Part III. This book provides structural evidence to support Einstein’s statement: “Quantum Mechanics is Incomplete!” forming the conjugate logic foundation of quantum measurements.

This book includes a wide range of topics from basic foundations to advanced applications. Different chapters may be suitable for special groups. For instance, Part I is useful for researchers and graduate students. Conjugate complex vector operators, symmetry/anti-symmetry brackets, Lie-Dirac-conjugate algebra, and conjugate combinatorial lattices are suitable for basic researchers on logic, probability, statistics, complex foundation, parallel synchronous time orders/modeling/analysis, complex analysis, complex geometric foundation, measures on mathematical foundation, combinatorial mathematics, meta-mathematics, quantum logic, and combinatorial group theory.

Part II is useful for the general audience on history development of complex conjugate numbers and quantum entanglement paradoxes. Richer visual maps of entangled experimental and simulated results are valuable for application researchers and engineers, senior college students and postgraduate students in quantum information, quantum communication, quantum computing, and quantum computers. Future applications are suitable for general researchers, engineers, and postgraduate and senior undergraduate students.

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Table of Contents



List of Contributor


Chapter 1. Conjugate Operators of Complex Vector Functions on Complex Number Plane — Parallel Time Synchronization Analysis ) => Pages 3-70
Jeffrey Zheng

Chapter 2. Measurement Operators of Conjugate Transformation Structure onComplex Plane — Conjugate Algebra on Pair 0–1 Feature Vectors and Symmetric/Anti-symmetric Brackets  => Pages 71-108
Jeffrey Zheng

Chapter 3. Conjugate Complex Measurements of Clock Reference Signals — ConjugateQuantum Numbers of Narrow and General Projections on Complex Number Plane => Pages 109-146
Jeffrey Zheng, Qi Wang, Yujin Lu, and Youping Li

Chapter 4. Combinatorial Lattice Clusters of Conjugate Complex VectorFunctions — Quantitative Distributions and Refined Measurements ofStrong Interactions on Complex Planes  => Pages 147-182
Jeffrey Zheng, Yangyang Tao, and Wanyi Zhou


Chapter 5. Modern Progress in Entangled Measurements of Quantum Optics — Entanglement States of Quantum Measurements on Geometric Transformations => Pages 185-250
Jeffrey Zheng and Jianzhong Liu

Chapter 6. Entanglement Foundation of Quantum Optics on Conjugate PhaseSpace — Three Measuring Models of Quantum Interactions on Conjugate Complex Vector Functions => Pages 251-306
Jeffrey Zheng, Fan Peng, Rui Wang, and Youping Li

Chapter 7. Conjugate Construction in Future Explorations — Resolved Logical Paradoxes on Multivariate Complex Functions and Hierarchical Structures => Pages 307-332
Jeffrey Zheng


A1.  Lemmas, Theorems, and Corollaries in Chapter 1

A2.  Lemmas, Theorems, and Corollaries in Chapter 2

A3.  Lemmas, Theorems, and Corollaries in Chapter 3

A4.  Lemmas, Theorems, and Corollaries in Chapter 4  

A5.  Lemmas and Corollaries in Chapter 5

A6.  Lemmas, Assumptions, Predictions, Theorems, and Corollaries in Chapter 6 

A7. Lemmas, Assumptions, Predictions, Theorems, and Corollaries in Chapter 7


Author’s ORCID iD

Jeffrey Zheng0000-0003-4225-7077

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