The quantum nature of the state of a bosonic quantum field may manifest itself in its entanglement, coherence, or optical nonclassicality. Each of these distinct properties is known to be a resource for quantum computing or metrology and can be evaluated via a variety of measures, witnesses, or monotones. Here, we provide quantitative and computable bounds relating, in particular, some entanglement measures with optical nonclassicality measures. Overall, these bounds capture the fact that strongly entangled states must necessarily be strongly optically nonclassical. As an application, we infer strong bounds on the entanglement that can be produced with an optically nonclassical state impinging on a beam splitter. Then, focusing on Gaussian states, we analyze the link between the logarithmic negativity and a specific nonclassicality measure called quadrature coherence scale.
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.
Nonclassicality of optical states, as a key characteristic of bosonic fields, is a valuable resource for quantum information processing. We investigate the generation of nonclassicality in quantum processes from a quantitative perspective, introduce three information-theoretic measures of nonclassicality for quantum-optical processes based on the Wigner–Yanase skew information and coherent states, and illustrate their physical significance through several well-known single-mode quantum processes.
The nonclassicality of quantum states is a fundamental resource for quantum technologies and quantum information tasks, in general. In particular, a pivotal aspect of quantum states lies in their coherence properties, encoded in the nondiagonal terms of their density matrix in the Fock-state bosonic basis. We present operational criteria to detect the nonclassicality of individual quantum coherences that use only data obtainable in experimentally realistic scenarios. We analyze and compare the robustness of the nonclassical coherence aspects when the states pass through lossy and noisy channels. The criteria can be immediately applied to experiments with light, atoms, solid-state system, and mechanical oscillators, thus providing a toolbox allowing practical experiments to more easily detect the nonclassicality of generated states.
Nonclassicality is an interesting property of light having applications in many different contexts of quantum optics, quantum information and computation. Nonclassical states produce substantial amount of reduced noise in optical communications. Furthermore, they often behave as sources of entangled quantum states, which are the most elementary requirement for quantum teleportation. We study various nonclassical properties of coherent states and Schrödinger cat states in a setting of noncommutative space resulting from the generalized uncertainty relation, first, in a complete analytical fashion and, later, by computing their entanglement entropies, which in turn provide supporting arguments behind our analytical results. By using standard theoretical frameworks, they are shown to produce considerably improved squeezing and nonclassicality and, hence, significantly higher amount of entanglement in comparison to the usual quantum mechanical models. Both the nonclassicality and the entanglement can be enhanced further by increasing the noncommutativity of the underlying space. In addition, we find as a by-product some rare explicit minimum uncertainty quadrature and number squeezed states, i.e., ideal squeezed states.
A bosonic state is commonly considered nonclassical (or quantum) if its Glauber-Sudarshan
P function is not a classical probability density, which implies that only coherent states and their statistical mixtures are classical. We quantify the nonclassicality of a single qubit, defined by the vacuum and single-photon states, by applying the following four well-known measures of nonclassicality: (1) the nonclassical depth, $\ensuremath{\tau}$, related to the minimal amount of Gaussian noise which changes a nonpositive
P function into a positive one; (2) the nonclassical distance
D, defined as the Bures distance of a given state to the closest classical state, which is the vacuum for the single-qubit Hilbert space; together with (3) the negativity potential (NP), and (4) concurrence potential, which are the nonclassicality measures corresponding to the entanglement measures (i.e., the negativity and concurrence, respectively) for the state generated by mixing a single-qubit state with the vacuum on a balanced beam splitter. We show that complete statistical mixtures of the vacuum and single-photon states are the most nonclassical single-qubit states regarding the distance
D for a fixed value of both the depth $\ensuremath{\tau}$ and NP in the whole range
[0,1] of their values, as well as the NP for a given value of $\ensuremath{\tau}$ such that $\ensuremath{\tau}>0.315\phantom{\rule{0.16em}{0ex}}4$. Conversely, pure states are the most nonclassical single-qubit states with respect to $\ensuremath{\tau}$ for a given
D, NP versus
D, and $\ensuremath{\tau}$ versus NP. We also show the ``relativity'' of these nonclassicality measures by comparing pairs of single-qubit states: if a state is less nonclassical than another state according to some measure then it might be more nonclassical according to another measure. Moreover, we find that the concurrence potential is equal to the nonclassical distance for single-qubit states. This implies an operational interpretation of the nonclassical distance as the potential for the entanglement of formation.