12,898 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
Quantum Communication Through an Unmodulated Spin Chain
We propose a scheme for using an unmodulated and unmeasured spin-chain as a
channel for short distance quantum communications. The state to be transmitted
is placed on one spin of the chain and received later on a distant spin with
some fidelity. We first obtain simple expressions for the fidelity of quantum
state transfer and the amount of entanglement sharable between any two sites of
an arbitrary Heisenberg ferromagnet using our scheme. We then apply this to the
realizable case of an open ended chain with nearest neighbor interactions. The
fidelity of quantum state transfer is obtained as an inverse discrete cosine
transform and as a Bessel function series. We find that in a reasonable time, a
qubit can be directly transmitted with better than classical fidelity across
the full length of chains of up to 80 spins. Moreover, the spin-chain channel
allows distillable entanglement to be shared over arbitrarily large distances.Comment: Much improved versio
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
Weighted Scale-free Networks in Euclidean Space Using Local Selection Rule
A spatial scale-free network is introduced and studied whose motivation has
been originated in the growing Internet as well as the Airport networks. We
argue that in these real-world networks a new node necessarily selects one of
its neighbouring local nodes for connection and is not controlled by the
preferential attachment as in the Barab\'asi-Albert (BA) model. This
observation has been mimicked in our model where the nodes pop-up at randomly
located positions in the Euclidean space and are connected to one end of the
nearest link. In spite of this crucial difference it is observed that the
leading behaviour of our network is like the BA model. Defining link weight as
an algebraic power of its Euclidean length, the weight distribution and the
non-linear dependence of the nodal strength on the degree are analytically
calculated. It is claimed that a power law decay of the link weights with time
ensures such a non-linear behavior. Switching off the Euclidean space from the
same model yields a much simpler definition of the Barab\'asi-Albert model
where numerical effort grows linearly with .Comment: 6 pages, 6 figure
Statistical Communication Theory
Contains reports on work completed and one research projects.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E)National Aeronautics and Space Administration (Grant NGR-22-009-304
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
Long-lived spin entanglement induced by a spatially correlated thermal bath
We investigate how two spatially separated qubits coupled to a common heat
bath can be entangled by purely dissipative dynamics. We identify a dynamical
time scale associated with the lifetime of the dissipatively generated
entanglement and show that it can be much longer than either the typical
single-qubit decoherence time or the time scale on which a direct exchange
interaction can entangle the qubits. We give an approximate analytical
expression for the long-time evolution of the qubit concurrence and propose an
ion trap scheme in which such dynamics should be observable.Comment: 5 pages, 2 figure
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
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