Geometric phases in dressed state quantum computation

Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations and how one may take advantage of the dressed states producing them. Specifically, we show that that for a given, but arbitrary Hamiltonian, and at an arbitrary time {\tau}, there always exists a set of dressed states such that a given gate operation can be performed by the Hamiltonian up to a phase {\phi}. The phase is a sum of a dynamical phase and a geometric phase. We illustrate the new phase for several systems.Comment: 4 pages, 2 figure

Implications of Qudit Superselection rules for the Theory of Decoherence-free Subsystems

The use of d-state systems, or qudits, in quantum information processing is discussed. Three-state and higher dimensional quantum systems are known to have very different properties from two-state systems, i.e., qubits. In particular there exist qudit states which are not equivalent under local unitary transformations unless a selection rule is violated. This observation is shown to be an important factor in the theory of decoherence-free, or noiseless, subsystems. Experimentally observable consequences and methods for distinguishing these states are also provided, including the explicit construction of new decoherence-free or noiseless subsystems from qutrits. Implications for simulating quantum systems with quantum systems are also discussed.Comment: 13 pages, 1 figures, Version 2: Typos corrected, references fixed and new ones added, also includes referees suggested changes and a new exampl

Casimir Invariants for Systems Undergoing Collective Motion

Dicke states are states of a collection of particles which have been under active investigation for several reasons. One reason is that the decay rates of these states can be quite different from a set of independently evolving particles. Another reason is that a particular class of these states are decoherence-free or noiseless with respect to a set of errors. These noiseless states, or more generally subsystems, can avoid certain types of errors in quantum information processing devices. Here we provide a method for calculating invariants of systems of particles undergoing collective motions. These invariants can be used to determine a complete set of commuting observables for a class of Dicke states as well as identify possible logical operations for decoherence-free/noiseless subsystems. Our method is quite general and provides results for cases where the constituent particles have more than two internal states.Comment: 5 page

Gamma Ray and Neutron Spectrometer for the Lunar Resource Mapper

One of the early Space Exploration Initiatives will be a lunar orbiter to map the elemental composition of the Moon. This mission will support further lunar exploration and habitation and will provide a valuable dataset for understanding lunar geological processes. The proposed payload will consist of the gamma ray and neutron spectrometers which are discussed, an x ray fluorescence imager, and possibly one or two other instruments

An Investigation into the Geometry of Seyfert Galaxies

We present a new method for the statistical investigation into the distributions of the angle beta between the radio axis and the normal to the galactic disk for a sample of Seyfert galaxies. We discuss how further observations of the sample galaxies can strengthen the conclusions. Our data are consistent with the hypothesis that AGN jets are oriented randomly in space, independent of the position of the plane of the galaxy. By making the simple assumption that the Standard Model of AGN holds, with a universal opening angle of the thick torus of phi_c, we demonstrate a statistical method to obtain an estimate of phi_c. Our data are not consistent with the simple-minded idea that Seyfert 1s and Seyfert 2s are differentiated solely by whether or not our line of sight lies within some fixed angle of the jet axis. Our result is significant on the 2 sigma level and can thus be considered only suggestive, not conclusive. A complete sample of Seyfert galaxies selected on an isotropic property is required to obtain a conclusive result.Comment: 13 pages, Tex, 5 Postscript figures. Accepted Ap

Topological structures of adiabatic phase for multi-level quantum systems

The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2) systems (e.g. two-level quantum system or angular momentum systems, etc) have a monopole structure, the curvature two-forms of the adiabatic holonomies for SU(3) three-level and SU(3) eight-level quantum systems are shown to have monopole-like (for all levels) or instanton-like (for the degenerate levels) structures.Comment: 15 pages, no figures. Accepted by J.Phys.

A Parametrization of Bipartite Systems Based on SU(4) Euler Angles

In this paper we give an explicit parametrization for all two qubit density matrices. This is important for calculations involving entanglement and many other types of quantum information processing. To accomplish this we present a generalized Euler angle parametrization for SU(4) and all possible two qubit density matrices. The important group-theoretical properties of such a description are then manifest. We thus obtain the correct Haar (Hurwitz) measure and volume element for SU(4) which follows from this parametrization. In addition, we study the role of this parametrization in the Peres-Horodecki criteria for separability and its corresponding usefulness in calculating entangled two qubit states as represented through the parametrization.Comment: 23 pages, no figures; changed title and abstract and rewrote certain areas in line with referee comments. To be published in J. Phys. A: Math. and Ge

Quasi-doubly periodic solutions to a generalized Lame equation

We consider the algebraic form of a generalized Lame equation with five free parameters. By introducing a generalization of Jacobi's elliptic functions we transform this equation to a 1-dim time-independent Schroedinger equation with (quasi-doubly) periodic potential. We show that only for a finite set of integral values for the five parameters quasi-doubly periodic eigenfunctions expressible in terms of generalized Jacobi functions exist. For this purpose we also establish a relation to the generalized Ince equation.Comment: 15 pages,1 table, accepted for publication in Journal of Physics