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Characterising optical quantum states is essential for the development of quantum technologies. While traditional approaches to perform full quantum state tomography are often experimentally demanding, neuromorphic architectures may provide…

This thesis focuses on three main questions in the continuous variable and optical settings: where does a quantum advantage, that is, the ability of quantum machines to outperform classical machines, come from? How to ensure the proper…

High-order quantum nonlinearity is an important prerequisite for the advanced quantum technology leading to universal quantum processing with large information capacity of continuous variables. Levitated optomechanics, a field where motion…

Superpositions of coherent light states, are vital for quantum technologies. However, restrictions in existing state preparation and characterization schemes, in combination with decoherence effects, prevent their intensity enhancement and…

The spectrum of vacuum fluctuations of the electromagnetic field is determined solely from first physical principles and can be seen as a fundamental property that qualifies as a primary radiation standard. We demonstrate that the amplitude…

The quantum nature of the state of a bosonic quantum field manifests itself in its entanglement, coherence, or optical nonclassicality which are each known to be resources for quantum computing or metrology. We provide quantitative and…

Many quantum systems exhibit high sensitivity to their initial conditions, where microscopic quantum fluctuations can significantly influence macroscopic observables. Understanding how quantum states may influence the behavior of nonlinear…

We consider a generic optomechanical system, consisting of a driven optical cavity and a movable mirror attached to a cantilever. Systems of this kind (and analogues) have been realized in many recent experiments. It is well known that…

Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system…

Quantum interferometry methods exploit quantum resources, such as photonic entanglement, to enhance phase estimation beyond classical limits. Nonlinear optics has served as a workhorse for the generation of entangled photon pairs, ensuring…

Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of "noncommutative fields". Our description permits to break the usual particle-antiparticle…

Rigorous derivations of the approach of individual elements of large isolated systems to a state of thermal equilibrium, starting from arbitrary initial states, are exceedingly rare. This is particularly true for quantum mechanical systems.…

The origin of non-classicality in physical systems and its connection to distinctly quantum features such as entanglement and coherence is a central question in quantum physics. This work analyses this question theoretically and…

Nonlinear interactions between single quantum particles are at the heart of any quantum information system, including analog quantum simulation and fault-tolerant quantum computing. This remains a particularly difficult problem for photonic…

Non-classical concerns light whose properties cannot be explained by classical electrodynamics and which requires invoking quantum principles to be understood. Its existence is a direct consequence of field quantization; its study is a…

The solution of one--dimensional asymmetric quantum harmonic oscillator is presented. The asymmetry can be realized, for example, by using two springs, one spring is glued with the mass, and the second spring is freely connected with the…

The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order…

Quantum light is considered to be one of the key resources of the coming second quantum revolution expected to give rise to groundbreaking technologies and applications. If the spatio-temporal and polarization structure of modes is known,…

This article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems. In presence of effective photon-photon interactions induced by…

Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices.…