Foundations of Quantum Optics for Quantum Information: Crash Course on Nonclassical States and Quantum Correlations

TL;DR

These notes present a concise, self-contained introduction to the foundations of quantum optics and their relevance to quantum information, emphasizing nonclassical states and quantum correlations. They connect field quantization, Fock space, and state descriptions (coherent, squeezed, thermal) to phase-space formalisms (P-function, Wigner, Q) and Gaussian-state theory, including the role of beam splitters in generating entanglement. The text integrates theory with practical tools, detailing operational criteria (Peres–Horodecki, Simon criterion, logarithmic negativity) and providing simulation labs using Strawberry Fields to model CV states, entanglement, and networked optical transformations. Altogether, the work offers a practical, theory-to-implementation bridge for students and researchers entering CV quantum information science, highlighting both conceptual foundations and computational approaches with real-world applicability.

Abstract

Nonclassical states of light and their correlations lie at the heart of quantum optics, serving as fundamental resources that underpin both the exploration of quantum phenomena and the realisation of quantum information protocols. These lecture notes provide an accessible yet rigorous introduction to the foundations of quantum optics, emphasising their relevance to quantum information science and technology. Starting from the quantisation of the electromagnetic field and the bosonic formalism of Fock space, the notes develop a unified framework for describing and analysing quantum states of light. Key families of states -- thermal, coherent, and squeezed -- are introduced as paradigmatic examples illustrating the transition from classical to nonclassical behaviour. The concepts of convexity, classicality, and quasiprobability representations are presented as complementary tools for characterising quantumness and defining operational notions such as P-nonclassicality. The discussion extends naturally to Gaussian states, composite systems, and continuous-variable entanglement, highlighting how nonclassicality serves as a resource for generating and quantifying quantum correlations. Theoretical developments are complemented by computational and experimental perspectives, including simulations of optical states using the Python library Strawberry Fields and data analysis from simulated data. Together, these notes aim to bridge the foundational concepts of quantum optics and modern quantum information, offering both conceptual insight and practical tools for students and researchers entering the field.

Figures (12)

• Figure 1: Illustrations of symmetric (coherent) and asymmetric (squeezed) quadrature uncertainties.
• Figure 2: Illustration of convex and non-convex sets using line-segment criteria.
• Figure 3: Quantum and classical (in the sense of P-non negativity) states form convex sets.
• Figure 4: Beam splitter model showing classical input and output field amplitudes.
• Figure 5: Squeezing condition for the variance of a squeezed vacuum state with real squeezing parameter r=1