$\bf{Abstract}$: A qubit lattice algorithm (QLA), which consists of a set interleaved unitary collision-streaming operators, is developed for electromagnetic wave propagation in tensor dielectric media. External potential operators are required to handle gradients the refractive indices, and these typically non-unitary. similar problem arises QLA Korteweg-de Vries equation, as operator that mod...

Starting from conventional Young operators we construct Hermitian operators which project orthogonally onto irreducible representations of the (special) unitary group.

Quantum entanglement plays a key role in quantum information theory. In recent years, there has been a lot of efforts to characterize the entanglement of quantum states both qualitatively and quantitatively. Entangled states can be generated from disentangled states by the action of a non-local Hamitonians. That means these Hamiltonians have the ability to entangle quantum states. It is therefo...

2 Linear Operators 6 2.1 Outer Products, Adjoints, and Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Important Types of Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 Projections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.2 Normal Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

A method for constructing dressing transformations for certain field theory models has been developed by Glimm. 1 This method employs a sequence of operators that are not unitary. In Refs. 2 and 3 an alternate construction is developed employing unitary operators. In Ref. 4 results are obtained on the equivalence of different dressing transformations constructed for ¢~+1 by the method of Glimm....

Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a line...

For an operator T in the class Bn(Ω), introduced in [4], the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle ET determine the unitary equivalence class of the operator T . In the paper [6], the authors ask if there exists some pair of inequivalent oprators T1 and T2 for which the simultaneous unitary equival...

We discuss a general strategy which produces an orthonormal set of vectors, stable under the action of a given set of unitary operators Aj , j = 1, 2, . . . , n, starting from a fixed normalized vector in H and from a set of unitary operators. We discuss several examples of this procedure and, in particular, we show how a set of coherent-like vectors can be produced and in which condition over ...

On one-dimensional two-way infinite lattice system, a property of stationary (space-) translationally invariant states with nonvanishing current expectations are investigated. We consider GNS representation with respect to such a state, on which we have a group of space-time translation unitary operators. We show, by applying Goldstone-theoremlike argument, that spectrum of the unitary operator...