Related papers: Three short tales on the parity operator
For bounded right linear operators, in a right quaternionic Hilbert space with a left multiplication defined on it, we study the approximate $S$-point spectrum. In the same Hilbert space, then we study the Fredholm operators and the…
The paper deals with a fractional derivative introduced by means of the Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the…
Wiener-Hopf plus Hankel operators acting between Lebesgue spaces on the real line are studied in view of their invertibility, one sided-invertibility, Fredholm, and semi-Fredholm properties. This is done in two different cases: (i) when the…
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…
Based on the matrix realignment and partial transpose, we develop an approach to entangling power and operator entanglement of quantum unitary operators. We demonstrate efficiency of the approach by studying several unitary operators on…
We demonstrate the applicability of a universal gate set in the parity encoding, which is a dual to the standard gate model, by exploring several quantum gate algorithms such as the quantum Fourier transform and quantum addition. Embedding…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications…
Second variation of a smooth optimal control problem at a regular extremal is a symmetric Fredholm operator. We study asymptotics of the spectrum of this operator and give an explicit expression for its determinant in terms of solutions of…
We show that the recently introduced operator fidelity metric provides a natural tool to investigate the cross-over to quantum chaotic behaviour. This metric is an information-theoretic measure of the global stability of a unitary evolution…
An odd Fredholm module for a given invertible operator on a Hilbert space is specified by an unbounded so-called Dirac operator with compact resolvent and bounded commutator with the given invertible. Associated to this is an index pairing…
Commuting is an important property in many cases of investigation of properties of operators as well as in various applications, especially in quantum physics. Using the observation that the generalized weighted differential operator of…
In this expository note, we present a simple proof of the Fredholm Alternative for compact operators that are norm limits of finite rank operators. We also prove a Fredholm Alternative for pseudodifferential operators of order < 0.
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
Characterizations of the star, minus and diamond orders of operators are given in various contexts and the relationship between these orders is made more transparent. Moreover, we introduce a new partial order of operators which provides a…
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators.…
The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented, and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The…
After a brief introduction recalling how, in the limit in which the mass and the electric charge of the electron and the positron tend to zero, Quantum Electrodynamics reduces to a collection of uncoupled quantum supersymmetric harmonic…
This is a brief survey which reviews some traditional themes in harmonic analysis and some more recent areas of activity, connected to "analysis on fractals" in particular.