2,070 research outputs found
Discrimination and synthesis of recursive quantum states in high-dimensional Hilbert spaces
We propose an interferometric method for statistically discriminating between
nonorthogonal states in high dimensional Hilbert spaces for use in quantum
information processing. The method is illustrated for the case of photon
orbital angular momentum (OAM) states. These states belong to pairs of bases
that are mutually unbiased on a sequence of two-dimensional subspaces of the
full Hilbert space, but the vectors within the same basis are not necessarily
orthogonal to each other. Over multiple trials, this method allows
distinguishing OAM eigenstates from superpositions of multiple such
eigenstates. Variations of the same method are then shown to be capable of
preparing and detecting arbitrary linear combinations of states in Hilbert
space. One further variation allows the construction of chains of states
obeying recurrence relations on the Hilbert space itself, opening a new range
of possibilities for more abstract information-coding algorithms to be carried
out experimentally in a simple manner. Among other applications, we show that
this approach provides a simplified means of switching between pairs of
high-dimensional mutually unbiased OAM bases
Local symmetry dynamics in one-dimensional aperiodic lattices
A unifying description of lattice potentials generated by aperiodic
one-dimensional sequences is proposed in terms of their local reflection or
parity symmetry properties. We demonstrate that the ranges and axes of local
reflection symmetry possess characteristic distributional and dynamical
properties which can be determined for every aperiodic binary lattice. A
striking aspect of such a property is given by the return maps of sequential
spacings of local symmetry axes, which typically traverse few-point symmetry
orbits. This local symmetry dynamics allows for a classification of inherently
different aperiodic lattices according to fundamental symmetry principles.
Illustrating the local symmetry distributional and dynamical properties for
several representative binary lattices, we further show that the renormalized
axis spacing sequences follow precisely the particular type of underlying
aperiodic order. Our analysis thus reveals that the long-range order of
aperiodic lattices is characterized in a compellingly simple way by its local
symmetry dynamics.Comment: 15 pages, 12 figure
Binary self-similar one-dimensional quasilattices: Mutual local-derivability classification and substitution rules
Self-similar binary one-dimensional (1D) quasilattices (QLs) are classified
into mutual local-derivability (MLD) classes. It is shown that the MLD
classification is closely related to the number-theoretical classification of
parameters which specify the self-similar binary 1D QLs. An algorithm to derive
an explicit substitution rule, which prescribes the transformation of a QL into
another QL in the same MLD class, is presented. An explicit inflation rule,
which prescribes the transformation of the self-similar 1D QL into itself, is
obtained as a composition of the explicit substitution rules. Symmetric
substitution rules and symmetric inflation rules are extensively discussed.Comment: 24 pages, 4 figures, submitted to PR
Knowledge-generating Efficiency in Innovation Systems: The relation between structural and temporal effects
Using time series of US patents per million inhabitants, knowledge-generating
cycles can be distinguished. These cycles partly coincide with Kondratieff long
waves. The changes in the slopes between them indicate discontinuities in the
knowledge-generating paradigms. The knowledge-generating paradigms can be
modeled in terms of interacting dimensions (for example, in
university-industry-government relations) that set limits to the maximal
efficiency of innovation systems. The maximum values of the parameters in the
model are of the same order as the regression coefficients of the empirical
waves. The mechanism of the increase in the dimensionality is specified as
self-organization which leads to the breaking of existing relations into the
more diversified structure of a fractal-like network. This breaking can be
modeled in analogy to 2D and 3D (Koch) snowflakes. The boost of knowledge
generation leads to newly emerging technologies that can be expected to be more
diversified and show shorter life cycles than before. Time spans of the
knowledge-generating cycles can also be analyzed in terms of Fibonacci numbers.
This perspective allows for forecasting expected dates of future possible
paradigm changes. In terms of policy implications, this suggests a shift in
focus from the manufacturing technologies to developing new organizational
technologies and formats of human interaction
Simulation of braiding anyons using Matrix Product States
Anyons exist as point like particles in two dimensions and carry braid
statistics which enable interactions that are independent of the distance
between the particles. Except for a relatively few number of models which are
analytically tractable, much of the physics of anyons remain still unexplored.
In this paper, we show how U(1)-symmetry can be combined with the previously
proposed anyonic Matrix Product States to simulate ground states and dynamics
of anyonic systems on a lattice at any rational particle number density. We
provide proof of principle by studying itinerant anyons on a one dimensional
chain where no natural notion of braiding arises and also on a two-leg ladder
where the anyons hop between sites and possibly braid. We compare the result of
the ground state energies of Fibonacci anyons against hardcore bosons and
spinless fermions. In addition, we report the entanglement entropies of the
ground states of interacting Fibonacci anyons on a fully filled two-leg ladder
at different interaction strength, identifying gapped or gapless points in the
parameter space. As an outlook, our approach can also prove useful in studying
the time dynamics of a finite number of nonabelian anyons on a finite
two-dimensional lattice.Comment: Revised version: 20 pages, 14 captioned figures, 2 new tables. We
have moved a significant amount of material concerning symmetric tensors for
anyons --- which can be found in prior works --- to Appendices in order to
streamline our exposition of the modified Anyonic-U(1) ansat
Effective models of doped quantum ladders of non-Abelian anyons
Quantum spin models have been studied extensively in one and higher
dimensions. Furthermore, these systems have been doped with holes to study
-- models of spin-1/2. Their anyonic counterparts can be built
from non-Abelian anyons, such as Fibonacci anyons described by
theories, which are quantum deformations of the algebra. Inspired by
the physics of spins, several works have explored ladders of Fibonacci
anyons and also one-dimensional (1D) -- models. Here we aim to explore
the combined effects of extended dimensionality and doping by studying ladders
composed of coupled chains of interacting itinerant Fibonacci anyons. We show
analytically that in the limit of strong rung couplings these models can be
mapped onto effective 1D models. These effective models can either be gapped
models of hole pairs, or gapless models described by -- (or modified
----) chains of Fibonacci anyons, whose spectrum exhibits a
fractionalization into charge and anyon degrees of freedom. By using exact
diagonalizations for two-leg and three-leg ladders, we show that indeed the
doped ladders show exactly the same behavior as that of -- chains. In the
strong ferromagnetic rung limit, we can obtain a new model that hosts two
different kinds of Fibonacci particles - which we denote as the heavy 's
and light 's. These two particle types carry the same (non-Abelian)
topological charge but different (Abelian) electric charges. Once again, we map
the two-dimensional ladder onto an effective chain carrying these heavy and
light 's. We perform a finite size scaling analysis to show the
appearance of gapless modes for certain anyon densities whereas a topological
gapped phase is suggested for another density regime.Comment: 26 pages, 23 figures, 5 table
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