Related papers: Embedding quantum and random optics in a larger fi…
Continuous symmetries generated with observables of a quantum theory in the Minkowski spacetime are discussed. An example of an originated in this way algebra of observables is the algebra of observables of the canonical quantum theory,…
Quantum mechanics is 'emergent' if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present…
We develop a notion of quantum observable for the general boundary formulation of quantum theory. This notion is adapted to spacetime regions rather than to hypersurfaces and naturally fits into the topological quantum field theory like…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
This is the extended version of a talk presented at the J.W.Goethe Universitaet Frankfurt a. M. and at the same time a preview at a forthcoming extensive publication on the same subject. It is shown that there is a common background…
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
We introduce the concept of a "classical observable" as an operator with vanishingly small quantum fluctuations on a set of density matrices. It is shown how to construct them for a time evolved pure state. The study of classical…
Local operators are the basic observables in quantum field theory which encode the physics observed by a local experimentalist. However, when gravity is dynamical, diffeomorphism symmetries are gauged which apparently obstructs a sensible…
This article introduces operator on operator regression in quantum probability. Here in the regression model, the response and the independent variables are certain operator valued observables, and they are linearly associated with unknown…
What is light and how to describe it has always been a central subject in physics. As our understanding has increased, so have our theories changed: Geometrical optics, wave optics and quantum optics are increasingly sophisticated…
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…
This chapter provides a non-technical overview and motivation for the recent interactions between algebraic quantum field theory (AQFT) and rather abstract mathematical disciplines such as operads, model categories and higher categories.
Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…
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,…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
We theoretically investigate quantum interference of two single photons at a lossy asymmetric beam splitter, the most general passive 2$\times$2 optical circuit. The losses in the circuit result in a non-unitary scattering matrix with a…
By putting together an abstract view on quantum mechanics and a quantum-optics picture of the interactions of an atom with light, we develop a corresponding set of C++ classes that set up the numerical analysis of an atom with an arbitrary…
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…
Optical homodyne tomography is discussed in the context of classical image processing. Analogies between these two fields are traced and used to formulate an iterative numerical algorithm for reconstructing the Wigner function from homodyne…