4,208 research outputs found
Teleportation Topology
We discuss the structure of teleportation. By associating matrices to the
preparation and measurement states, we show that for a unitary transformation M
there is a full teleportation procedure for obtaining M|S> from a given state
|S>. The key to this construction is a diagrammatic intepretation of matrix
multiplication that applies equally well to a topological composition of a
maximum and a minimum that underlies the structure of the teleportation. This
paper is a preliminary report on joint work with H. Carteret and S. Lomonaco.Comment: LaTeX document, 16 pages, 8 figures, Talk delivered at the Xth
International Conference on Quantum Optics, Minsk, Belaru
Teleportation, Braid Group and Temperley--Lieb Algebra
We explore algebraic and topological structures underlying the quantum
teleportation phenomena by applying the braid group and Temperley--Lieb
algebra. We realize the braid teleportation configuration, teleportation
swapping and virtual braid representation in the standard description of the
teleportation. We devise diagrammatic rules for quantum circuits involving
maximally entangled states and apply them to three sorts of descriptions of the
teleportation: the transfer operator, quantum measurements and characteristic
equations, and further propose the Temperley--Lieb algebra under local unitary
transformations to be a mathematical structure underlying the teleportation. We
compare our diagrammatical approach with two known recipes to the quantum
information flow: the teleportation topology and strongly compact closed
category, in order to explain our diagrammatic rules to be a natural
diagrammatic language for the teleportation.Comment: 33 pages, 19 figures, latex. The present article is a short version
of the preprint, quant-ph/0601050, which includes details of calculation,
more topics such as topological diagrammatical operations and entanglement
swapping, and calls the Temperley--Lieb category for the collection of all
the Temperley--Lieb algebra with physical operations like local unitary
transformation
Particle Topology, Braids, and Braided Belts
Recent work suggests that topological features of certain quantum gravity
theories can be interpreted as particles, matching the known fermions and
bosons of the first generation in the Standard Model. This is achieved by
identifying topological structures with elements of the framed Artin braid
group on three strands, and demonstrating a correspondence between the
invariants used to characterise these braids (a braid is a set of
non-intersecting curves, that connect one set of points with another set of
points), and quantities like electric charge, colour charge, and so on. In
this paper we show how to manipulate a modified form of framed braids to yield
an invariant standard form for sets of isomorphic braids, characterised by a
vector of real numbers. This will serve as a basis for more complete
discussions of quantum numbers in future work.Comment: 21 pages, 16 figure
Polynomial knot and link invariants from the virtual biquandle
The Alexander biquandle of a virtual knot or link is a module over a
2-variable Laurent polynomial ring which is an invariant of virtual knots and
links. The elementary ideals of this module are then invariants of virtual
isotopy which determine both the generalized Alexander polynomial (also known
as the Sawollek polynomial) for virtual knots and the classical Alexander
polynomial for classical knots. For a fixed monomial ordering , the
Gr\"obner bases for these ideals are computable, comparable invariants which
fully determine the elementary ideals and which generalize and unify the
classical and generalized Alexander polynomials. We provide examples to
illustrate the usefulness of these invariants and propose questions for future
work.Comment: 12 pages; version 3 includes corrected figure
A solvable model of the evolutionary loop
A model for the evolution of a finite population in a rugged fitness
landscape is introduced and solved. The population is trapped in an
evolutionary loop, alternating periods of stasis to periods in which it
performs adaptive walks. The dependence of the average rarity of the population
(a quantity related to the fitness of the most adapted individual) and of the
duration of stases on population size and mutation rate is calculated.Comment: 6 pages, EuroLaTeX, 1 figur
The Asymptotic Number of Attractors in the Random Map Model
The random map model is a deterministic dynamical system in a finite phase
space with n points. The map that establishes the dynamics of the system is
constructed by randomly choosing, for every point, another one as being its
image. We derive here explicit formulas for the statistical distribution of the
number of attractors in the system. As in related results, the number of
operations involved by our formulas increases exponentially with n; therefore,
they are not directly applicable to study the behavior of systems where n is
large. However, our formulas lend themselves to derive useful asymptotic
expressions, as we show.Comment: 16 pages, 1 figure. Minor changes. To be published in Journal of
Physics A: Mathematical and Genera
An analytic Approach to Turaev's Shadow Invariant
In the present paper we extend the "torus gauge fixing approach" by Blau and
Thompson (Nucl. Phys. B408(1):345--390, 1993) for Chern-Simons models with base
manifolds M of the form M= \Sigma x S^1 in a suitable way. We arrive at a
heuristic path integral formula for the Wilson loop observables associated to
general links in M. We then show that the right-hand side of this formula can
be evaluated explicitly in a non-perturbative way and that this evaluation
naturally leads to the face models in terms of which Turaev's shadow invariant
is defined.Comment: 44 pages, 2 figures. Changes have been made in Sec. 2.3, Sec 2.4,
Sec. 3.4, and Sec. 3.5. Appendix C is ne
Annealing schedule from population dynamics
We introduce a dynamical annealing schedule for population-based optimization
algorithms with mutation. On the basis of a statistical mechanics formulation
of the population dynamics, the mutation rate adapts to a value maximizing
expected rewards at each time step. Thereby, the mutation rate is eliminated as
a free parameter from the algorithm.Comment: 6 pages RevTeX, 4 figures PostScript; to be published in Phys. Rev.
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