Quantum Optics Advances Nonclassical States & Correlations for Information Technology

Nonclassical states of light and the quantum correlations they exhibit are crucial for advancing both fundamental physics and quantum technologies. Jhoan Eusse from Universidad de Antioquia, Esteban Vasquez and Tom Rivlin from TU Wien, along with Elizabeth Agudelo, present a comprehensive overview of these concepts, offering a vital ‘crash course’ for those entering the field. Their work establishes a rigorous foundation in quantum optics, beginning with the quantisation of light and progressing to detailed analyses of thermal, coherent and squeezed states , illuminating the shift from classical to nonclassical behaviour. Significantly, these lecture notes bridge the gap between foundational optical principles and their application to quantum information science, providing both theoretical insight and practical tools via Python-based simulations and data analysis.

Their work establishes a rigorous foundation in Quantum optics, beginning with the quantisation of light and progressing to detailed analyses of thermal, coherent and squeezed states, illuminating the shift from classical to nonclassical behaviour. Significantly, these lecture notes bridge the gap between foundational optical principles and their application to Quantum information science, providing both theoretical insight and practical tools via Python-based simulations and data analysis. Scientists are increasingly recognising nonclassical states of light and their correlations as fundamental resources underpinning quantum optics and quantum information science.

Researchers at the Universidad de Antioquia and TU Wien collaborated on this work, aiming to consolidate key principles for both established researchers and newcomers to the field. The approach involves a comprehensive review and pedagogical presentation of relevant theoretical frameworks, including those concerning the generation and characterisation of nonclassical light. Specific contributions detail the properties of squeezed states, entangled photons, and other exotic states of light, alongside methods for quantifying quantum correlations such as entanglement and discord. The work highlights the importance of these states for applications in quantum key distribution, quantum computation, and quantum sensing.
Scientists are increasingly exploring 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 representation are also discussed.

Quantum technologies progress from theory to application

Scientists are increasingly focused on quantum technologies, confirmed to extraordinary precision in countless experiments. It not only explains phenomena classical physics cannot, like superconductivity, lasers, and the structure of matter, but also underpins technologies shaping everyday life, including transistors, medical imaging, and emerging quantum computers. 2025 was labeled the International Year of Quantum Science and Technology, celebrating achievements and highlighting the transformative role quantum physics is expected to play this century. Quantum technologies have rapidly advanced over the past two decades, transitioning from theoretical concepts to experimental demonstrations and early commercial applications. Today, they encompass superconducting circuits, trapped ions, photonics, and spin-based systems, each with distinct strengths in correlation times, scalability and controllability.

Quantum sensing and metrology have reached remarkable precision, exploiting quantum phenomena such as entanglement and squeezing to surpass classical limits in detecting magnetic fields and gravitational waves, and in setting time standards. Quantum communication, particularly through quantum key distribution, has moved toward secure, real-world networks, with satellite-based implementations already demonstrating global reach. The pursuit of quantum computing has seen significant milestones, with small-scale universal quantum processors achieving tens to hundreds to thousands of qubits. While error rates and decoherence remain challenges, algorithms for quantum simulation, optimization, and cryptography are being actively developed.

The concept of quantum advantage, where a quantum device performs a task beyond the practical reach of classical computers, has been experimentally demonstrated in specialized scenarios, such as random circuit sampling and boson sampling. However, fully general-purpose quantum advantage, especially for applications of widespread practical significance, is still far on the horizon, as fault-tolerant architectures and error-corrected qubits will be required for reliable, large-scale computation, and these remain out of reach for now. Overall, the field is at a transformative stage: experimental capabilities are rapidly maturing, and theoretical progress continues to identify problems where quantum resources can provide meaningful speedups or precision gains. The convergence of hardware development, algorithmic innovation, and applications in secure communication, simulation, and sensing positions quantum technologies to potentially revolutionize computation, information processing, and measurement science, although significant technical and engineering challenges remain before broad quantum advantage is realized.

Quantum information theory provides the fundamental framework underpinning quantum technologies. Formalising how information is encoded, processed, and transmitted using quantum systems defines the principles behind quantum computing, quantum communication, and quantum sensing. Concepts such as superposition, qubits, and entanglement are directly derived from this theory, guiding the design of algorithms, protocols, and devices that exploit uniquely quantum effects for quantum advantages. In essence, quantum information theory acts as both the roadmap and the rulebook for turning quantum phenomena into practical technologies.

Quantum information theory relies on reinterpreting the principles of quantum mechanics through an information-theoretic lens. Tasks such as storing, processing, and transmitting information are inherently tied to the physical properties of the systems in which the information is encoded. As a result, physics, information, and computation are deeply interconnected. The initial extension of classical information science into the quantum domain naturally focused on qubits, the quantum analogues of classical bits. Early on, it became evident that uniquely quantum effects, such as superposition and entanglement, provide significant advantages for information processing, enabling tasks to be performed faster, more efficiently, and with higher precision.

Light is an exciting platform for quantum technologies due to the wide range of available experimental tools and techniques. For decades, laser sources, beam splitters, interferometers, and single-photon detectors have enabled the precise preparation, manipulation, and measurement of quantum states of light in relatively inexpensive, easily constructed laboratory settings. These tools enable fundamental experiments that explore the boundary between classical and quantum physics, such as tests of superposition, contextuality, nonlocality, entanglement, and other quantum correlations. Photonics also integrates naturally with emerging technologies like integrated photonic circuits, offering scalability and miniaturization that are crucial for building practical quantum devices.

Finally, optics allows direct visualization and experimental control of quantum phenomena, which is both scientifically exciting and technologically promising. Optical systems can simulate complex quantum systems, test quantum algorithms, and explore quantum-enhanced sensing and metrology with unprecedented precision. This combination of fundamental insight, practical applicability, and elegant experimental accessibility makes optics a particularly attractive and “cool” platform for advancing quantum technologies and pushing the boundaries of what quantum systems can achieve. The cornerstone of quantum optics, and the fundamental source of quantum effects for quantum technologies, is the quantum states of light and their correlations.

Throughout this document, we introduce and discuss these states, providing a crash course on the foundations of quantum optics for quantum information, with a focus on nonclassical states and quantum correlations. There exists an extensive collection of excellent textbooks on quantum optics and quantum information where these topics are discussed in great detail. In these notes, we have curated a selection of concepts and results with the aim of providing a self-contained introduction to optical nonclassicality and its connection to quantum correlations. We first build the foundations by introducing the quantization of the electromagnetic field and its description in terms of harmonic oscillator modes, and by reviewing the bosonic formalism of Fock space and second quantization. We then turn to specific families of quantum states, beginning with the coherent states often regarded as the “most classical” quantum states and continuing with squeezed states and their role as paradigmatic examples of nonclassical light. The discussion is then broadened to include mixed states, convexity and criteria for classicality, and the characterization of states through their quasiprobability distributions.

Nonclassical Light, Quantum States and Entanglement are fundamental

Scientists have developed a comprehensive framework for understanding nonclassical states of light and their role in quantum information science. These lecture notes detail the quantisation of the electromagnetic field, utilising the bosonic formalism of Fock space to analyse quantum states. Key light states , thermal, coherent, and squeezed , are presented to illustrate the shift from classical to nonclassical behaviour, with concepts like convexity, classicality, and quasiprobability representations used to characterise quantumness. The work extends to Gaussian states, composite systems, and continuous-variable entanglement, demonstrating how nonclassicality generates and quantifies quantum correlations.

Theoretical analysis is supported by computational tools, including simulations using the Python library Strawberry Fields and analysis of simulated data. Authors acknowledge limitations inherent in modelling complex quantum systems and suggest future research could explore the practical implementation of these states in advanced quantum technologies. This research establishes a robust foundation linking foundational optics with modern quantum information, offering valuable insights and practical tools for researchers and students entering the field.