22,095 research outputs found
Sharp Quantum vs. Classical Query Complexity Separations
We obtain the strongest separation between quantum and classical query
complexity known to date -- specifically, we define a black-box problem that
requires exponentially many queries in the classical bounded-error case, but
can be solved exactly in the quantum case with a single query (and a polynomial
number of auxiliary operations). The problem is simple to define and the
quantum algorithm solving it is also simple when described in terms of certain
quantum Fourier transforms (QFTs) that have natural properties with respect to
the algebraic structures of finite fields. These QFTs may be of independent
interest, and we also investigate generalizations of them to noncommutative
finite rings.Comment: 13 pages, change in title, improvements in presentation, and minor
corrections. To appear in Algorithmic
Aharonov-Bohm interference in quantum ring exciton: effects of built-in electric fields
We report a comprehensive discussion of quantum interference effects due to
the finite structure of excitons in quantum rings and their first experimental
corroboration observed in the optical recombinations. Anomalous features that
appear in the experiments are analyzed according to theoretical models that
describe the modulation of the interference pattern by temperature and built-in
electric fields.Comment: 6 pages, 7 figure
Schemes as functors on topological rings
Let be a scheme. In this text, we extend the known definitions of a
topology on the set of -rational points from topological fields,
local rings and ad\`ele rings to any ring with a topology. This definition
is functorial in both and , and it does not rely on any restriction on
like separability or finiteness conditions. We characterize properties of
, such as being a topological Hausdorff ring, a local ring or having
as an open subset for which inversion is continuous, in terms of
functorial properties of the topology of . Particular instances of this
general approach yield a new characterization of adelic topologies, and a
definition of topologies for higher local fields.Comment: 14 page
Hard isogeny problems over RSA moduli and groups with infeasible inversion
We initiate the study of computational problems on elliptic curve isogeny
graphs defined over RSA moduli. We conjecture that several variants of the
neighbor-search problem over these graphs are hard, and provide a comprehensive
list of cryptanalytic attempts on these problems. Moreover, based on the
hardness of these problems, we provide a construction of groups with infeasible
inversion, where the underlying groups are the ideal class groups of imaginary
quadratic orders.
Recall that in a group with infeasible inversion, computing the inverse of a
group element is required to be hard, while performing the group operation is
easy. Motivated by the potential cryptographic application of building a
directed transitive signature scheme, the search for a group with infeasible
inversion was initiated in the theses of Hohenberger and Molnar (2003). Later
it was also shown to provide a broadcast encryption scheme by Irrer et al.
(2004). However, to date the only case of a group with infeasible inversion is
implied by the much stronger primitive of self-bilinear map constructed by
Yamakawa et al. (2014) based on the hardness of factoring and
indistinguishability obfuscation (iO). Our construction gives a candidate
without using iO.Comment: Significant revision of the article previously titled "A Candidate
Group with Infeasible Inversion" (arXiv:1810.00022v1). Cleared up the
constructions by giving toy examples, added "The Parallelogram Attack" (Sec
5.3.2). 54 pages, 8 figure
Charged Annular Disks and Reissner-Nordstr\"{o}m Type Black Holes from Extremal Dust
We present the first analytical superposition of a charged black hole with an
annular disk of extremal dust. In order to obtain the solutions, we first solve
the Einstein-Maxwell field equations for sources that represent disk-like
configurations of matter in confomastatic spacetimes by assuming a functional
dependence among the metric function, the electric potential and an auxiliary
function,which is taken as a solution of the Laplace equation. We then employ
the Lord Kelvin Inversion Method applied to models of finite extension in order
to obtain annular disks. The structures obtained extend to infinity, but their
total masses are finite and all the energy conditions are satisfied. Finally,
we observe that the extremal Reissner-Nordstr\"{o}m black hole can be embedded
into the center of the disks by adding a boundary term in the inversion.Comment: 17 revtex pages, 8 eps figure
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