2,935 research outputs found
A Bloch-Sphere-Type Model for Two Qubits in the Geometric Algebra of a 6-D Euclidean Vector Space
Geometric algebra is a mathematical structure that is inherent in any metric
vector space, and defined by the requirement that the metric tensor is given by
the scalar part of the product of vectors. It provides a natural framework in
which to represent the classical groups as subgroups of rotation groups, and
similarly their Lie algebras. In this article we show how the geometric algebra
of a six-dimensional real Euclidean vector space naturally allows one to
construct the special unitary group on a two-qubit (quantum bit) Hilbert space,
in a fashion similar to that used in the well-established Bloch sphere model
for a single qubit. This is then used to illustrate the Cartan decompositions
and subalgebras of the four-dimensional special unitary group, which have
recently been used by J. Zhang, J. Vala, S. Sastry and K. B. Whaley [Phys. Rev.
A 67, 042313, 2003] to study the entangling capabilities of two-qubit
unitaries.Comment: 14 pages, 2 figures, in press (Proceedings of SPIE Conference on
Defense & Security
A Superfield for Every Dash-Chromotopology
The recent classification scheme of so-called adinkraic off-shell
supermultiplets of N-extended worldline supersymmetry without central charges
finds a combinatorial explosion. Completing our earlier efforts, we now
complete the constructive proof that all of these trillions or more of
supermultiplets have a superfield representation. While different as
superfields and supermultiplets, these are still super-differentially related
to a much more modest number of minimal supermultiplets, which we construct
herein.Comment: 13 pages, integrated illustration
Matrix Transfer Function Design for Flexible Structures: An Application
The application of matrix transfer function design techniques to the problem of disturbance rejection on a flexible space structure is demonstrated. The design approach is based on parameterizing a class of stabilizing compensators for the plant and formulating the design specifications as a constrained minimization problem in terms of these parameters. The solution yields a matrix transfer function representation of the compensator. A state space realization of the compensator is constructed to investigate performance and stability on the nominal and perturbed models. The application is made to the ACOSSA (Active Control of Space Structures) optical structure
Reflection Symmetries for Multiqubit Density Operators
For multiqubit density operators in a suitable tensorial basis, we show that
a number of nonunitary operations used in the detection and synthesis of
entanglement are classifiable as reflection symmetries, i.e., orientation
changing rotations. While one-qubit reflections correspond to antiunitary
symmetries, as is known for example from the partial transposition criterion,
reflections on the joint density of two or more qubits are not accounted for by
the Wigner Theorem and are well-posed only for sufficiently mixed states. One
example of such nonlocal reflections is the unconditional NOT operation on a
multiparty density, i.e., an operation yelding another density and such that
the sum of the two is the identity operator. This nonphysical operation is
admissible only for sufficiently mixed states.Comment: 9 page
New Techniques for Analysing Axisymmetric Gravitational Systems. 1. Vacuum Fields
A new framework for analysing the gravitational fields in a stationary,
axisymmetric configuration is introduced. The method is used to construct a
complete set of field equations for the vacuum region outside a rotating
source. These equations are under-determined. Restricting the Weyl tensor to
type D produces a set of equations which can be solved, and a range of new
techniques are introduced to simplify the problem. Imposing the further
condition that the solution is asymptotically flat yields the Kerr solution
uniquely. The implications of this result for the no-hair theorem are
discussed. The techniques developed here have many other applications, which
are described in the conclusions.Comment: 30 pages, no figure
Fermion absorption cross section of a Schwarzschild black hole
We study the absorption of massive spin-half particles by a small
Schwarzschild black hole by numerically solving the single-particle Dirac
equation in Painleve-Gullstrand coordinates. We calculate the absorption cross
section for a range of gravitational couplings Mm/m_P^2 and incident particle
energies E. At high couplings, where the Schwarzschild radius R_S is much
greater than the wavelength lambda, we find that the cross section approaches
the classical result for a point particle. At intermediate couplings we find
oscillations around the classical limit whose precise form depends on the
particle mass. These oscillations give quantum violations of the equivalence
principle. At high energies the cross section converges on the geometric-optics
value of 27 \pi R_S^2/4, and at low energies we find agreement with an
approximation derived by Unruh. When the hole is much smaller than the particle
wavelength we confirm that the minimum possible cross section approaches \pi
R_S^2/2.Comment: 11 pages, 3 figure
Effective Symmetries of the Minimal Supermultiplet of N = 8 Extended Worldline Supersymmetry
A minimal representation of the N = 8 extended worldline supersymmetry, known
as the `ultra-multiplet', is closely related to a family of supermultiplets
with the same, E(8) chromotopology. We catalogue their effective symmetries and
find a Spin(4) x Z(2) subgroup common to them all, which explains the
particular basis used in the original construction. We specify a constrained
superfield representation of the supermultiplets in the ultra-multiplet family,
and show that such a superfield representation in fact exists for all adinkraic
supermultiplets. We also exhibit the correspondences between these
supermultiplets, their Adinkras and the E(8) root lattice bases. Finally, we
construct quadratic Lagrangians that provide the standard kinetic terms and
afford a mixing of an even number of such supermultiplets controlled by a
coupling to an external 2-form of fluxes.Comment: 13 Figure
Quadratic Lagrangians and Topology in Gauge Theory Gravity
We consider topological contributions to the action integral in a gauge
theory formulation of gravity. Two topological invariants are found and are
shown to arise from the scalar and pseudoscalar parts of a single integral.
Neither of these action integrals contribute to the classical field equations.
An identity is found for the invariants that is valid for non-symmetric Riemann
tensors, generalizing the usual GR expression for the topological invariants.
The link with Yang-Mills instantons in Euclidean gravity is also explored. Ten
independent quadratic terms are constructed from the Riemann tensor, and the
topological invariants reduce these to eight possible independent terms for a
quadratic Lagrangian. The resulting field equations for the parity
non-violating terms are presented. Our derivations of these results are
considerably simpler that those found in the literature
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