Scholarlink

This chapter is devoted to the description of quantum optics and continuous variables (CV) concepts relevant in quantum communications and QKD. The chapter starts with electromagnetic waves, vector potential, and wave equation. The quantizing of electromagnetic fields is described next. After an introduction of the quadrature operators, Fock, coherent, and squeezed states are introduced. The beam splitter is described next quantum mechanically, and it is used to build the homodyne balanced detector. The quantum Mach–Zehnder interferometer is introduced next, followed by the thermal radiation states. The chapter continues with the introduction of fundamentals of the Gaussian quantum information theory, where the P-representation is introduced and applied to represent the thermal noise as well as the thermal noise plus the coherent state signal. Further, Gaussian states are introduced, followed by Wigner function definition as well as the definition of correlation matrices. The next section is devoted to the Gaussian transformation and Gaussian channels, with beam splitter operation, phase rotation operation, and squeezing operators being the representative examples. The thermal decomposition of Gaussian states is discussed next, and the von Neumann entropy for thermal states is derived. The focus is then moved to the nonlinear quantum optics fundamentals, in particular the three-wave mixing and four-wave mixing are described in detail. Further, generation of the Gaussian states is described, and two-mode squeeze state generation is discussed in detail. The correlation matrices for two-mode Gaussian states are discussed next, and how to calculate the symplectic eigenvalues, relevant in von Neumann entropy calculation. The Gaussian states measurements and detection are discussed then, with emphasis on homodyne detection, heterodyne detection, and partial measurements. The covariance matrices for multimode Gaussian states are introduced next. After the set of problems, the final section of the chapter provides some relevant concluding remarks.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Quantum Optics and Continuous Variables (CV) Fundamentals

  • 章节

  • 发表日期：

    2025年

查看全文
  • Ivan B. Djordjevic

摘要

This chapter is devoted to the description of quantum optics and continuous variables (CV) concepts relevant in quantum communications and QKD. The chapter starts with electromagnetic waves, vector potential, and wave equation. The quantizing of electromagnetic fields is described next. After an introduction of the quadrature operators, Fock, coherent, and squeezed states are introduced. The beam splitter is described next quantum mechanically, and it is used to build the homodyne balanced detector. The quantum Mach–Zehnder interferometer is introduced next, followed by the thermal radiation states. The chapter continues with the introduction of fundamentals of the Gaussian quantum information theory, where the P-representation is introduced and applied to represent the thermal noise as well as the thermal noise plus the coherent state signal. Further, Gaussian states are introduced, followed by Wigner function definition as well as the definition of correlation matrices. The next section is devoted to the Gaussian transformation and Gaussian channels, with beam splitter operation, phase rotation operation, and squeezing operators being the representative examples. The thermal decomposition of Gaussian states is discussed next, and the von Neumann entropy for thermal states is derived. The focus is then moved to the nonlinear quantum optics fundamentals, in particular the three-wave mixing and four-wave mixing are described in detail. Further, generation of the Gaussian states is described, and two-mode squeeze state generation is discussed in detail. The correlation matrices for two-mode Gaussian states are discussed next, and how to calculate the symplectic eigenvalues, relevant in von Neumann entropy calculation. The Gaussian states measurements and detection are discussed then, with emphasis on homodyne detection, heterodyne detection, and partial measurements. The covariance matrices for multimode Gaussian states are introduced next. After the set of problems, the final section of the chapter provides some relevant concluding remarks.