Related papers: Quantum Reference Frames on Homogeneous Spaces
In this paper fields of quantum reference frames based on gauge transformations of rational string states are described in a way that, hopefully, makes them more understandable than their description in an earlier paper. The approach taken…
We explain the powerful role that operator-valued measures can play in quantizing any set equipped with a measure, for instance a group (resp. group coset) with its invariant (resp. quasi-invariant) measure. Coherent state quantization is a…
Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling…
The quantum space-time model which accounts material Reference Frames (RF) quantum effects considered for flat space-time and ADM canonical gravity. As was shown by Aharonov for RF - free material object its c.m. nonrelativistic motion in…
Reference frames are used to parameterize measurements of physical effects, but since their practical realization uses material objects, they may affect observations performed in a combined quantum state of the measured system together with…
The intention of this thesis is to provide general tools and concepts that allow to perform a mathematically substantiated symmetry reduction in (quantum) gauge field theories. Here, the main focus is on the framework of loop quantum…
Encoding classical data into quantum states is considered a quantum feature map to map classical data into a quantum Hilbert space. This feature map provides opportunities to incorporate quantum advantages into machine learning algorithms…
Recently, fusion frames and frames for operators were considered as generalizations of frames in Hilbert spaces. In this paper, we generalize some of the known results in frame theory to fusion frames related to a linear bounded operator K…
Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.
This thesis is a compilation of research in relativistic quantum information theory, and research in quantum reference frames. The research in the former category provides a fundamental construction of quantum information theory of…
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…
We introduce Quantum Time-Frequency Analysis, which expands the approach of Quantum Harmonic Analysis to include modulations of operators in addition to translations. This is done by a projective representation of double-phase space, and we…
Relativistic quantum field theory (QFT) is commonly formulated in terms of operators, asymptotic states, and covariant amplitudes, a perspective that tends to obscure the real-time origin of field dynamics and correlations. Here we…
Quotient regularization models (QRMs) are a class of powerful regularization techniques that have gained considerable attention in recent years, due to their ability to handle complex and highly nonlinear data sets. However, the nonconvex…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
A significant step towards a rigorous understanding of perturbative gravitational entropy was recently achieved by a series of works showing that a proper accounting of gauge invariance and observer degrees of freedom converts the Type III…
This work introduces a novel three-fold classification of reference frames in General Relativity, distinguishing between Idealised Reference Frames (IRFs), Dynamical Reference Frames (DRFs), and Real Reference Frames (RRFs). By defining a…
Krein space quantization and the ambient space formalism have been successfully applied to address challenges in quantum geometry (e.g., quantum gravity) and the axiomatic formulation of quantum Yang-Mills theory, including phenomena such…