1,182 research outputs found
Optimizing local protocols implementing nonlocal quantum gates
We present a method of optimizing recently designed protocols for
implementing an arbitrary nonlocal unitary gate acting on a bipartite system.
These protocols use only local operations and classical communication with the
assistance of entanglement, and are deterministic while also being "one-shot",
in that they use only one copy of an entangled resource state. The optimization
is in the sense of minimizing the amount of entanglement used, and it is often
the case that less entanglement is needed than with an alternative protocol
using two-way teleportation.Comment: 11 pages, 1 figure. This is a companion paper to arXiv:1001.546
Conformal approach to cylindrical DLA
We extend the conformal mapping approach elaborated for the radial Diffusion
Limited Aggregation model (DLA) to the cylindrical geometry. We introduce in
particular a complex function which allows to grow a cylindrical cluster using
as intermediate step a radial aggregate. The grown aggregate exhibits the same
self-affine features of the original cylindrical DLA. The specific choice of
the transformation allows us to study the relationship between the radial and
the cylindrical geometry. In particular the cylindrical aggregate can be seen
as a radial aggregate with particles of size increasing with the radius. On the
other hand the radial aggregate can be seen as a cylindrical aggregate with
particles of size decreasing with the height. This framework, which shifts the
point of view from the geometry to the size of the particles, can open the way
to more quantitative studies on the relationship between radial and cylindrical
DLA.Comment: 16 pages, 8 figure
On Free Quotients of Complete Intersection Calabi-Yau Manifolds
In order to find novel examples of non-simply connected Calabi-Yau
threefolds, free quotients of complete intersections in products of projective
spaces are classified by means of a computer search. More precisely, all
automorphisms of the product of projective spaces that descend to a free action
on the Calabi-Yau manifold are identified.Comment: 39 pages, 3 tables, LaTe
Schlaganfall aus der Perspektive des Neurologen (Teil 3): Neues in der Sekundärprävention
In dieser dritten Ausgabe über den Schlaganfall wird die Sekundärprävention besprochen. Nach der Akutphase mit ihren Massnahmen zur Wiedereröffnung eines verschlossenen Hirngefässes schenkt man der Prävention eines erneuten Schlaganfalls und wenn möglich der Frührehabilitation die volle Aufmerksamkeit. Aus der Perspektive des Neurologen ist eine systematische Diagnostik, eine erweiterte Abklärung der (nicht-)modifizierbaren Risikofaktoren und eine mit der Klinik und Bildgebung integrierte präventive Therapie dringend erforderlich. Neben der optimalen Einstellung der wichtigen therapierbaren Risikofaktoren wie arterielle Hypertonie, Vorhofflimmern, Diabetes mellitus und Dyslipidämie sind auch die Behandlung des obstruktiven Schlafapnoe-Syndroms und komplexer Atheromatosen (komplexe Plaque der Aorta >4 mm [1]) als eigenständige Risikofaktoren erwiesen. Die Suche nach der Ätiologie geht meist nach der Definition der Wahrscheinlichkeit verschiedener Ursachen. Die wahrscheinlichste wird dann als Ursache angenommen. Nur in seltenen Fällen findet sich keine Ursache. Dann kann das Läsionsmuster helfen, zumindest zwischen embolischem und thrombotischem Ereignis zu unterscheiden.
In this third edition the secondary prevention of stroke will be discussed. After the acute phase in which recanalization of an occluded brain artery is in the focus, the risks for a recurrent stroke have to be minimized and rehabilitation should be started. A systematic workup, an extended evaluation of (non-) modifiable risk factors and the clinical-radiological findings are the source of an effective preventive therapy. Risk assessment of the major risk factors such as arterial hypertension, atrial fibrillation, diabetes and dyslipidemia is established. The obstructive sleep apnea syndrome and the complex atheromatosis with a complex structure are independent risk factors for stroke. The search for an etiology is usually a definition of probabilities. The most probable cause of stroke is assumed
Decomposition of fractional quantum Hall states: New symmetries and approximations
We provide a detailed description of a new symmetry structure of the monomial
(Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall
states first obtained in Ref. 1, which we now extend to spin-singlet states. We
show that the Haldane-Rezayi spin-singlet state can be obtained without exact
diagonalization through a differential equation method that we conjecture to be
generic to other FQH model states. The symmetry rules in Ref. 1 as well as the
ones we obtain for the spin singlet states allow us to build approximations of
FQH states that exhibit increasing overlap with the exact state (as a function
of system size). We show that these overlaps reach unity in the thermodynamic
limit even though our approximation omits more than half of the Hilbert space.
We show that the product rule is valid for any FQH state which can be written
as an expectation value of parafermionic operators.Comment: 22 pages, 8 figure
Covariant Quantum Fields on Noncommutative Spacetimes
A spinless covariant field on Minkowski spacetime \M^{d+1} obeys the
relation where
is an element of the Poincar\'e group \Pg and is its unitary representation on quantum vector states. It
expresses the fact that Poincar\'e transformations are being unitary
implemented. It has a classical analogy where field covariance shows that
Poincar\'e transformations are canonically implemented. Covariance is
self-reproducing: products of covariant fields are covariant. We recall these
properties and use them to formulate the notion of covariant quantum fields on
noncommutative spacetimes. In this way all our earlier results on dressing,
statistics, etc. for Moyal spacetimes are derived transparently. For the Voros
algebra, covariance and the *-operation are in conflict so that there are no
covariant Voros fields compatible with *, a result we found earlier. The notion
of Drinfel'd twist underlying much of the preceding discussion is extended to
discrete abelian and nonabelian groups such as the mapping class groups of
topological geons. For twists involving nonabelian groups the emergent
spacetimes are nonassociative.Comment: 20 page
On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spaces
Let g=g_0+g_1 be a Z_2-graded Lie algebra. We study the posets of abelian
subalgebras of g_1 which are stable w.r.t. a Borel subalgebra of g_0. In
particular, we find out a natural parametrization of maximal elements and
dimension formulas for them. We recover as special cases several results of
Kostant, Panyushev, Suter.Comment: Latex file, 35 pages, minor corrections, some examples added. To
appear in Selecta Mathematic
On the multiplicativity of quantum cat maps
The quantum mechanical propagators of the linear automorphisms of the
two-torus (cat maps) determine a projective unitary representation of the theta
group, known as Weil's representation. We prove that there exists an
appropriate choice of phases in the propagators that defines a proper
representation of the theta group. We also give explicit formulae for the
propagators in this representation.Comment: Revised version: proof of the main theorem simplified. 21 page
Schur Q-functions and degeneracy locus formulas for morphisms with symmetries
We give closed-form formulas for the fundamental classes of degeneracy loci
associated with vector bundle maps given locally by (not necessary square)
matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal.
Our description uses essentially Schur Q-polynomials of a bundle, and is based
on a certain push-forward formula for these polynomials in a Grassmann bundle.Comment: 22 pages, AMSTEX, misprints corrected, exposition improved. to appear
in the Proceedings of Intersection Theory Conference in Bologna, "Progress in
Mathematics", Birkhause
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