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

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.

💡 Research Summary

The manuscript “Foundations of Quantum Optics for Quantum Information: Crash Course on Nonclassical States and Quantum Correlations” is a comprehensive set of lecture notes that bridges the fundamental theory of quantum optics with its applications in quantum information science. It begins by motivating the importance of light as a versatile carrier for both discrete‑variable (DV) and continuous‑variable (CV) quantum protocols, emphasizing the recent surge in quantum technologies and the need for a clear pedagogical treatment of nonclassical optical states.

The authors first quantize a single electromagnetic mode confined in a one‑dimensional cavity, showing that the field Hamiltonian reduces to that of a harmonic oscillator, (H=\frac12(p^2+\omega^2x^2)). By promoting the canonical variables to operators and introducing the ladder operators (\hat a) and (\hat a^\dagger) with (