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The measurement processes that are traditionally described within the realm of non-relativistic quantum mechanics are transcribed into the covariant framework of Cartan's space, the four-valued representation space of the restricted…
We present a barycentric decomposition for quantum instruments whose output space is finite-dimensional and input space is separable. As a special case, we obtain a barycentric decomposition for channels between such spaces and for…
We show that norms on certain Banach spaces $X$ can be approximated uniformly, and with arbitrary precision, on bounded subsets of $X$ by $C^{\infty}$ smooth norms and polyhedral norms. In particular, we show that this holds for any…
In a previous work arXiv:physics/0611108v2, it was shown that the volume spanned by a molecular system in its conformational space can be effectively bounded by a polyhedral cone, this cone is described by means of a simple combinatorial…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
We explore the conceptual usefulness of Riemannian geometric tools induced by the statistical concept of distinguishability in quantifying the effect of a depolarizing channel on quantum states. Specifically, we compare the geometries of…
For many implementations of quantum computing, 1/f and other types of broad-spectrum noise are an important source of decoherence. An important step forward would be the ability to back out the characteristics of this noise from qubit…
In the literature, frames generated by unitary representations of groups (known as group-frames) are studied only for Hilbert spaces. We make first study of frames for Banach spaces generated by isometric invertible representations of…
We study quantum decoherence numerically in a system consisting of a relativistic quantum field theory coupled to a measuring device that is itself coupled to an environment. The measuring device and environment are treated as quantum,…
We prove a generalized implicit function theorem for Banach spaces, without the usual assumption that the subspaces involved being complemented. Then we apply it to the problem of parametrization of fibers of differentiable maps, the Lie…
We illustrate through numerical results a number of features of environment-induced decoherence under a broad class of apparatus-environment interactions in quantum measurements wherein the reduced system-apparatus density matrix evolves…
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…
We characterize the polynomial decay of orbits of Hilbert space $C_0$-semigroups in resolvent terms. We also show that results of the same type for general Banach space semigroups and functions obtained recently in the paper by C.J.K.Batty…
The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the…
The aim of the paper is to create a link between the theory of reproducing kernel Hilbert spaces (RKHS) and the notion of a unitary representation of a group or of a groupoid. More specifically, it is demonstrated on one hand, how to…
The concept of bock-coherence, first introduced in [1] and developed in [2,3] encompasses the case where experimental capabilities are not so delicate to perform arbitrary refined measurements on individual atoms. We develop a framework…
The ability to design quantum systems that decouple from environmental noise sources is highly desirable for development of quantum technologies with optimal coherence. The chemical tunability of electronic states in magnetic molecules…
We describe our recent results on the resonant perturbation theory of decoherence and relaxation for quantum system with many qubits. The approach represents a rigorous analysis of the phenomenon of decoherence and relaxation for general…
Coherence is a fundamental notion in quantum mechanics, defined relative to a reference basis. As such, it does not necessarily reveal the locality of interactions nor takes into account the accessible operations in a composite quantum…
In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class…