12,258 research outputs found
Lower bounds on the dilation of plane spanners
(I) We exhibit a set of 23 points in the plane that has dilation at least
, improving the previously best lower bound of for the
worst-case dilation of plane spanners.
(II) For every integer , there exists an -element point set
such that the degree 3 dilation of denoted by in the domain of plane geometric spanners. In the
same domain, we show that for every integer , there exists a an
-element point set such that the degree 4 dilation of denoted by
The
previous best lower bound of holds for any degree.
(III) For every integer , there exists an -element point set
such that the stretch factor of the greedy triangulation of is at least
.Comment: Revised definitions in the introduction; 23 pages, 15 figures; 2
table
On the normalization of Killing vectors and energy conservation in two-dimensional gravity
We explicitly show that, in the context of a recently proposed 2D dilaton
gravity theory, energy conservation requires the ``natural'' Killing vector to
have, asymptotically, an unusual normalization. The Hawking temperature
is then calculated according to this prescription.Comment: 7 pages, Latex, no figure
Reproducing spin lattice models in strongly coupled atom-cavity systems
In an array of coupled cavities where the cavities are doped with an atomic
V-system, and the two excited levels couple to cavity photons of different
polarizations, we show how to construct various spin models employed in
characterizing phenomena in condensed matter physics, such as the spin-1/2
Ising, XX, Heisenberg, and XXZ models. The ability to construct networks of
arbitrary geometry also allows for the simulation of topological effects. By
tuning the number of excitations present, the dimension of the spin to be
simulated can be controlled, and mixtures of different spin types produced. The
facility of single-site addressing, the use of only the natural hopping photon
dynamics without external fields, and the recent experimental advances towards
strong coupling, makes the prospect of using these arrays as efficient quantum
simulators promising.Comment: 4 pages, 3 figures. v3: References adde
Finding passwords by random walks: How long does it take?
We compare an efficiency of a deterministic "lawnmower" and random search
strategies for finding a prescribed sequence of letters (a password) of length
M in which all letters are taken from the same Q-ary alphabet. We show that at
best a random search takes two times longer than a "lawnmower" search.Comment: To appear in J. Phys. A, special issue on "Random Search Problem:
Trends and Perspectives", eds.: MEG da Luz, E Raposo, GM Viswanathan and A
Grosber
Teleportation as a Depolarizing Quantum Channel, Relative Entropy and Classical Capacity
We show that standard teleportation with an arbitrary mixed state resource is
equivalent to a generalized depolarizing channel with probabilities given by
the maximally entangled components of the resource. This enables the usage of
any quantum channel as a generalized depolarizing channel without additional
twirling operations. It also provides a nontrivial upper bound on the
entanglement of a class of mixed states. Our result allows a consistent and
statistically motivated quantification of teleportation success in terms of the
relative entropy and this quantification can be related to a classical
capacity.Comment: Version published in Phys. Rev. Let
Entanglement Concentration Using Quantum Statistics
We propose an entanglement concentration scheme which uses only the effects
of quantum statistics of indistinguishable particles. This establishes the fact
that useful quantum information processing can be accomplished by quantum
statistics alone. Due to the basis independence of statistical effects, our
protocol requires less knowledge of the initial state than most entanglement
concentration schemes. Moreover, no explicit controlled operation is required
at any stage.Comment: 2 figure
Critical energy flux and mass in solvable theories of 2d dilaton gravity
In this paper we address the issue of determining the semiclassical threshold
for black hole formation in the context of a one-parameter family of theories
which continuously interpolates between the RST and BPP models. We find that
the results depend significantly on the initial static configuration of the
spacetime geometry before the influx of matter is turned on. In some cases
there is a critical energy density, given by the Hawking rate of evaporation,
as well as a critical mass (eventually vanishing). In others there is
neither nor a critical flux.Comment: LaTeX file, 12 pages, 4 figure
Solving the Graceful Exit Problem in Superstring Cosmology
We briefly review the status of the ``graceful exit'' problem in superstring
cosmology and present a possible resolution. It is shown that there exists a
solution to this problem in two-dimensional dilaton gravity provided quantum
corrections are incorporated. This is similar to the recently proposed solution
of Rey. However, unlike in his case, in our one-loop corrected model the
graceful exit problem is solved for any finite number of massless scalar matter
fields present in the theory.Comment: 8 pages, RevTex. Based on talk given at Conference on Big Bang and
Alternative Cosmologies: A Critical Appraisal, Bangalore, India, January,
199
Quantum communication between trapped ions through a dissipative environment
We study two trapped ions coupled to the axial phonon modes of a
one-dimensional Coulomb crystal. This system is formally equivalent to the "two
spin-boson" model. We propose a scheme to dynamically generate a maximally
entangled state of two ions within a decoherence-free subspace. Here the
phononic environment of the trapped ions, whatever its temperature and number
of modes, serves as the entangling bus. The efficient production of the pure
singlet state can be exploited to perform short-ranged quantum communication
which is essential in building up a large-scale quantum computer.Comment: 4 pages, 2 figure
Vacuum entanglement governs the bosonic character of magnons
It is well known that magnons, elementary excitations in a magnetic material,
behave as bosons when their density is low. We study how the bosonic character
of magnons is governed by the amount of a multipartite entanglement in the
vacuum state on which magnons are excited. We show that if the multipartite
entanglement is strong, magnons cease to be bosons. We also consider some
examples, such as ground states of the Heisenberg ferromagnet and the
transverse Ising model, the condensation of magnons, the one-way quantum
computer, and Kitaev's toric code. Our result provides insights into the
quantum statistics of elementary excitations in these models, and into the
reason why a non-local transformation, such as the Jordan-Wigner
transformation, is necessary for some many-body systems.Comment: 4 pages, no figur
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