The chapter discusses the formulation of classical statistical decision and estimation theory in quantum-mechanical terms, focusing on the detection of signals in random noise and the estimation of parameters. The key concepts include density operators, which replace probability density functions in classical statistics, and the use of commuting observables for measurements. The chapter covers binary decisions, threshold detection, and the detection of coherent signals in thermal radiation. It also explores the quantum counterpart of the classical threshold statistic and the detection of Gaussian radiation. The text highlights the challenges and limitations of quantum detection theory, particularly in practical applications, and discusses the translation of quantum detection theory into forms suitable for optical instruments like telescopes. Additionally, it touches on the problem of choosing among multiple hypotheses and the estimation of parameters in quantum systems.The chapter discusses the formulation of classical statistical decision and estimation theory in quantum-mechanical terms, focusing on the detection of signals in random noise and the estimation of parameters. The key concepts include density operators, which replace probability density functions in classical statistics, and the use of commuting observables for measurements. The chapter covers binary decisions, threshold detection, and the detection of coherent signals in thermal radiation. It also explores the quantum counterpart of the classical threshold statistic and the detection of Gaussian radiation. The text highlights the challenges and limitations of quantum detection theory, particularly in practical applications, and discusses the translation of quantum detection theory into forms suitable for optical instruments like telescopes. Additionally, it touches on the problem of choosing among multiple hypotheses and the estimation of parameters in quantum systems.