相关论文: Chow's theorem and universal holonomic quantum com…
We derive, from first principles, the complete Luttinger liquid theory of abelian quantum Hall edge states. This theory includes the effects of disorder and Coulomb interactions as well as the coupling to external electromagnetic fields. We…
We propose an implementation scheme for holonomic, i.e., geometrical, quantum information processing based on semiconductor nanostructures. Our quantum hardware consists of coupled semiconductor macroatoms addressed/controlled by ultrafast…
In this note we construct bi-*-Galois objects linking the quantized universal enveloping algebras associated to the Lie groups SU(2), E(2) and SU(1,1), where E(2) denotes the Lie group of Euclidian transformations of the plane, and we show…
The gate version of quantum computation exploits several quantum key resources as superposition and entanglement to reach an outstanding performance. In the way, this theory was constructed adopting certain supposed processes imitating…
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…
The purpose of this paper is to introduce several basic theorems of coherent states and generalized coherent states based on Lie algebras su(2) and su(1,1), and to give some applications of them to quantum information theory for graduate…
In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each…
The Lie product and the order relation are viewed as defining structures for Hamiltonian dynamical systems. Their admissible combinations are singled out by the requirement that the group of the Lie automorphisms be contained in the group…
In the past few years there has been a tumultuous activity aimed at introducing novel conceptual schemes for quantum computing. The approach proposed in (Marzuoli A and Rasetti M 2002, 2005a) relies on the (re)coupling theory of SU(2)…
We describe a broad dynamical-algebraic framework for analyzing the quantum control properties of a set of naturally available interactions. General conditions under which universal control is achieved over a set of subspaces/subsystems are…
S. L. Woronowicz's theory of introducing C*-algebras generated by unbounded elements is applied to q-normal operators satisfying the defining relation of the quantum complex plane. The unique non-degenerate C*-algebra of bounded operators…
Four-level systems in quantum optics, and for representing two qubits in quantum computing, are difficult to solve for general time-dependent Hamiltonians. A systematic procedure is presented which combines analytical handling of the…
Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for…
Two-qubit logical gates are proposed on the basis of two atoms trapped in a cavity setup. Losses in the interaction by spontaneous transitions are efficiently suppressed by employing adiabatic transitions and the Zeno effect. Dynamical and…
In this paper we extend the Lie theory of integration in two different ways. First we consider a finite dimensional Lie algebra of vector fields and discuss the most general conditions under which the integral curves of one of the fields…
Any quantum computational network can be constructed with a sequence of the two-qubit diagonal quantum gates and one-qubit gates in two-state quantum systems. The universal construction of these quantum gates in the quantum systems and of…
A gauged $SU_q(2)$ theory is characterized by two dual algebras, the first lying close to the Lie algebra of SU(2) while the second introduces new degrees of freedom that may be associated with non-locality or solitonic structure. The first…
We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model…
Quantum information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control on the way quantum dynamics unfolds in the information-processing system. In…
Let us consider a Lie (super)algebra $G$ spanned by $T_{\alpha}$ where $T_{\alpha}$ are quantum observables in BV-formalism. It is proved that for every tensor $c^{\alpha_1...\alpha_k}$ that determines a homology class of the Lie algebra…