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Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
In the paper (math-ph/0504049) Jarlskog gave an interesting simple parametrization to unitary matrices, which was essentially the canonical coordinate of the second kind in the Lie group theory (math-ph/0505047). In this paper we apply the…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…
This article presents a new proof of a theorem concerning bounds of the spectrum of the product of unitary operators and a generalization for differentiable curves of this theorem. The proofs involve metric geometric arguments in the group…
It is well known that an (in general, non-commutative) set of non-Hermitian operators $\Lambda_j$ with real eigenvalues need not necessarily represent observables. We describe a specific class of quantum models in which these operators plus…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
We develop several methods, based on the geometric relationship between the eigenspaces of a matrix and its adjoint, for determining whether a square matrix having distinct eigenvalues is unitarily equivalent to a complex symmetric matrix.…
We present a brief review of discrete structures in a finite Hilbert space, relevant for the theory of quantum information. Unitary operator bases, mutually unbiased bases, Clifford group and stabilizer states, discrete Wigner function,…
This paper gives an introduction to the physics and principles of operation of quantized superconducting electrical circuits for quantum information processing.
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
In this article, we discard the bra-ket notation and its correlative definitions, given by Paul Dirac. The quantum states are only described by the wave functions. The fundamental concepts and definitions in quantum mechanics is simplified.…
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation…
It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that…
It is shown that an operator can be defined in the abstract space of random matrices ensembles whose matrix elements statistical distribution simulates the behavior of the distribution found in real physical systems. It is found that the…
Engineering quantum operations is one of the main abilities we need for developing quantum technologies and designing new fundamental tests. Here we propose a scheme for realising a controlled operation acting on a travelling quantum field,…
The classical Hilbert space formulation of the axioms of Quantum Mechanics appears to leave open the question whether the Hermitian operators which are associated with the observables of a finite non-relativistic quantum system are uniquely…
We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few body operators in chaotic many-body…
Students in quantum mechanics class are taught that the wave function contains all knowable information about an isolated system. Later in the course, this view seems to be contradicted by the mysterious density matrix, which introduces a…