Chapter 5 - Quantum detection and quantum communication

Abstract

This chapter focuses on quantum detection theory (QDT), quantum communication, and Gaussian quantum information theory. After briefly reviewing density operators, we describe QDT concepts and apply them to the binary detection problem. We introduce coherent states and describe their basic properties, followed by an introduction to quadrature operators and derivation of the uncertainty principle for continuous-variable systems. We then discuss binary quantum optical communication without noise, including photon-counting, on–off keying (OOK), binary phase-shift keying (BPSK), and Kennedy and Dolinar receivers. We discuss the P-representation and apply it to represent thermal noise and coherent states in the presence of thermal noise, followed by a discussion of binary optical communication in the presence of noise with a focus on OOK and BPSK. Gaussian and squeezed states are introduced, followed by definitions of the Wigner function and covariance matrices. Gaussian transformation and Gaussian channels are discussed, with beam splitter operation, phase rotation operation, and squeezing operator as examples. The thermal decomposition of Gaussian states is discussed, and the von Neumann entropy for thermal states is derived. Covariance matrices for two-mode Gaussian states are discussed in detail. Gaussian state measurements and detection are discussed, emphasizing homodyne detection, heterodyne detection, and partial measurements. The focus then moves to nonlinear quantum optics fundamentals; in particular, three-wave and four-wave mixing are described. The generation of Gaussian states is also described, and two-mode squeezed state generation is discussed in detail. Finally, we discuss multilevel quantum optical communication, wherein scenarios are described in the absence and presence of noise. Using square root measurements to analyze the performance of these schemes is described in detail.