Related papers: On the operator-sum formalism
Finite plane geometry is associated with finite dimensional Hilbert space. The association allows mapping of q-number Hilbert space observables to the c-number formalism of quantum mechanics in phase space. The mapped entities reflect…
Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…
It is known that local operators in quantum field theory transform in representations of ordinary global symmetry groups. The purpose of this paper is to generalise this statement to extended operators such as line and surface defects. We…
We show that all non-relativistic quantum processes, whether open or closed, are either unitary or probabilistic unitary, i.e., probabilistic combination of unitary evolutions. This means that for open quantum systems, its continuous…
In this paper a system-oriented formalism of Quantum Information Processing is presented. Its form resembles that of standard signal processing, although further complexity is added in order to describe pure quantum-mechanical effects and…
Relativistic quantum systems that admit scattering experiments are quantitatively described by effective field theories, where $S$-matrix kinematics and symmetry considerations are encoded in the operator spectrum of the EFT. In this paper…
In this paper we study shorted operators relative to two different subspaces, for bounded operators on infinite dimensional Hilbert spaces. We define two notions of complementability in the sense of Ando for operators, and study the…
This paper provides a short introduction to the mathematical foundation of quantum computation for researchers in computer science by providing an introduction fo the mathematical basis of calculations. This paper concerns the mathematical…
Nature provides us with a restricted set of microscopic interactions. The question is whether we can synthesize out of these fundamental interactions an arbitrary unitary operator. In this paper we present a constructive algorithm for…
The Quantum Query Model is a framework that allows us to express most known quantum algorithms. Algorithms represented by this model consist on a set of unitary operators acting over a finite Hilbert space, and a final measurement step…
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…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…
In this note, we develop a framework to describe open quantum systems in the Heisenberg picture, i.e., via time evolving operator algebras. We point out the incompleteness of the previous proposals in this regard. We argue that a complete…
Since Shor's discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers - the difficulty of…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
We introduce unbounded strongly irreducible operators and transitive operators. These operators are related to a certain class of indecomposable Hilbert representations of quivers on infinite-dimensional Hilbert spaces. We regard the theory…
We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately.…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…