Related papers: Finite tight frames and some applications
In this article, we present a new characterization of the completeness of a partial metric space--which we call \textit{orbital characterization}-- using fixed point results.
Decomposition of (finite-dimensional) operators in terms of orthogonal bases of matrices has been a standard method in quantum physics for decades. In recent years, it has become increasingly popular because of various methodologies applied…
We provide a sufficient condition for a finite number of closed subspaces of a Hilbert space to be linearly independent and their sum to be closed. Under this condition a formula for the orthogonal projection onto the sum is given. We also…
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…
In this paper, we obtain some new properties of weaving frames and present some conditions under which a family of frames is woven in Hilbert spaces. Some characterizations of weaving frames in terms of operators are given. We also give a…
Frames in a separable quaternionic Hilbert space were introduced and studied in [17] to have more applications. In this paper, we extend the study of frames in quaternionic Hilbert spaces and introduce different types of duals of a frame in…
We will show that tight frames satisfying the restricted isometry property give rise to nearly tight fusion frames which are nearly orthogonal and hence are nearly equi-isoclinic. We will also show how to replace parts of the RIP frame with…
In this work is discussed possibility and actuality of Lagrangian approach to quantum computations. Finite-dimensional Hilbert spaces used in this area provide some challenge for such consideration. The model discussed here can be…
Let $\hil$ be a finite dimensional (real or complex) Hilbert space and let $\{a_i\}_{i=1}^\infty$ be a non-increasing sequence of positive numbers. Given a finite sequence of vectors $\f$ in $\hil$ we find necessary and sufficient…
A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with…
High-dimensional Hilbert spaces possess large information encoding and transmission capabilities. Characterizing exactly the real potential of high-dimensional entangled systems is a cornerstone of tomography and quantum imaging. The…
We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to…
We reassess the problem of separability of the kinematic Hilbert space in loop quantum gravity under a new mathematical point of view. We use the formalism of frames, a tool used in signal analysis, in order to remove the redundancy of the…
We provide formulas for projectors onto a polyhedral set, i.e. the intersection of a finite number of halfspaces. To this aim we formulate the problem of finding the projection as a convex optimization problem and we solve explicitly…
The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the…
Extending the concept of frame to continuous frame, in this manuscript we will show that under certain conditions on the measure of $\Omega$ and the dimension of $\h$ we can construct continuous frames. Also, some examples are given.
In this paper, we have stated some results about this concept. Furthermore, we introduce the notion of controlled $E$-frames and we characterize all controlled $E$-duals associated with a given controlled $E$-frame.
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…