4,893 research outputs found
Higher Gauge Theory and Gravity in (2+1) Dimensions
Non-abelian higher gauge theory has recently emerged as a generalization of
standard gauge theory to higher dimensional (2-dimensional in the present
context) connection forms, and as such, it has been successfully applied to the
non-abelian generalizations of the Yang-Mills theory and 2-form
electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a
fertile testing ground for many concepts related to classical and quantum
gravity, and it is therefore only natural to investigate whether we can find an
application of higher gauge theory in this latter context. In the present paper
we investigate the possibility of applying the formalism of higher gauge theory
to gravity in (2+1) dimensions, and we show that a nontrivial model of
(2+1)-dimensional gravity coupled to scalar and tensorial matter fields - the
model - can be formulated both as a standard gauge theory and
as a higher gauge theory. Since the model has a very rich structure - it admits
as solutions black-hole BTZ-like geometries, particle-like geometries as well
as Robertson-Friedman-Walker cosmological-like expanding geometries - this
opens a wide perspective for higher gauge theory to be tested and understood in
a relevant gravitational context. Additionally, it offers the possibility of
studying gravity in (2+1) dimensions coupled to matter in an entirely new
framework.Comment: 22 page
Violations of local realism by two entangled quNits
Results obtained in two recent papers, \cite{Kaszlikowski} and \cite{Durt},
seem to indicate that the nonlocal character of the correlations between the
outcomes of measurements performed on entangled systems separated in space is
not robust in the presence of noise. This is surprising, since entanglement
itself is robust. Here we revisit this problem and argue that the class of
gedanken-experiments considered in \cite{Kaszlikowski} and \cite{Durt} is too
restrictive. By considering a more general class, involving sequences of
measurements, we prove that the nonlocal correlations are in fact robust.Comment: Reference added, 3 pages, accepted for publication in J. Phys. A:
Math. and Genera
Quantum privacy amplification and the security of quantum cryptography over noisy channels
Existing quantum cryptographic schemes are not, as they stand, operable in
the presence of noise on the quantum communication channel. Although they
become operable if they are supplemented by classical privacy-amplification
techniques, the resulting schemes are difficult to analyse and have not been
proved secure. We introduce the concept of quantum privacy amplification and a
cryptographic scheme incorporating it which is provably secure over a noisy
channel. The scheme uses an `entanglement purification' procedure which,
because it requires only a few quantum Controlled-Not and single-qubit
operations, could be implemented using technology that is currently being
developed. The scheme allows an arbitrarily small bound to be placed on the
information that any eavesdropper may extract from the encrypted message.Comment: 13 pages, Latex including 2 postcript files included using psfig
macro
Exact and Asymptotic Measures of Multipartite Pure State Entanglement
In an effort to simplify the classification of pure entangled states of multi
(m) -partite quantum systems, we study exactly and asymptotically (in n)
reversible transformations among n'th tensor powers of such states (ie n copies
of the state shared among the same m parties) under local quantum operations
and classical communication (LOCC). With regard to exact transformations, we
show that two states whose 1-party entropies agree are either locally-unitarily
(LU) equivalent or else LOCC-incomparable. In particular we show that two
tripartite Greenberger-Horne-Zeilinger (GHZ) states are LOCC-incomparable to
three bipartite Einstein-Podolsky-Rosen (EPR) states symmetrically shared among
the three parties. Asymptotic transformations result in a simpler
classification than exact transformations. We show that m-partite pure states
having an m-way Schmidt decomposition are simply parameterizable, with the
partial entropy across any nontrivial partition representing the number of
standard ``Cat'' states (|0^m>+|1^m>) asymptotically interconvertible to the
state in question. For general m-partite states, partial entropies across
different partitions need not be equal, and since partial entropies are
conserved by asymptotically reversible LOCC operations, a multicomponent
entanglement measure is needed, with each scalar component representing a
different kind of entanglement, not asymptotically interconvertible to the
other kinds. In particular the m=4 Cat state is not isentropic to, and
therefore not asymptotically interconvertible to, any combination of bipartite
and tripartite states shared among the four parties. Thus, although the m=4 cat
state can be prepared from bipartite EPR states, the preparation process is
necessarily irreversible, and remains so even asymptotically.Comment: 13 pages including 3 PostScript figures. v3 has updated references
and discussion, to appear Phys. Rev.
Anisotropic Diffusion Limited Aggregation
Using stochastic conformal mappings we study the effects of anisotropic
perturbations on diffusion limited aggregation (DLA) in two dimensions. The
harmonic measure of the growth probability for DLA can be conformally mapped
onto a constant measure on a unit circle. Here we map preferred directions
for growth of angular width to a distribution on the unit circle which
is a periodic function with peaks in such that the width
of each peak scales as , where defines the
``strength'' of anisotropy along any of the chosen directions. The two
parameters map out a parameter space of perturbations that allows a
continuous transition from DLA (for or ) to needle-like fingers
as . We show that at fixed the effective fractal dimension of
the clusters obtained from mass-radius scaling decreases with
increasing from to a value bounded from below by
. Scaling arguments suggest a specific form for the dependence
of the fractal dimension on for large , form which compares
favorably with numerical results.Comment: 6 pages, 4 figures, submitted to Phys. Rev.
Recovery of entanglement lost in entanglement manipulation
When an entangled state is transformed into another one with probability one
by local operations and classical communication, the quantity of entanglement
decreases. This letter shows that entanglement lost in the manipulation can be
partially recovered by an auxiliary entangled pair. As an application, a
maximally entangled pair can be obtained from two partially entangled pairs
with probability one. Finally, this recovery scheme reveals a fundamental
property of entanglement relevant to the existence of incomparable states.Comment: 4 pages, 2 figures, REVTeX; minor correction
Dynamic entanglement in oscillating molecules and potential biological implications
We demonstrate that entanglement can persistently recur in an oscillating
two-spin molecule that is coupled to a hot and noisy environment, in which no
static entanglement can survive. The system represents a non-equilibrium
quantum system which, driven through the oscillatory motion, is prevented from
reaching its (separable) thermal equilibrium state. Environmental noise,
together with the driven motion, plays a constructive role by periodically
resetting the system, even though it will destroy entanglement as usual. As a
building block, the present simple mechanism supports the perspective that
entanglement can exist also in systems which are exposed to a hot environment
and to high levels of de-coherence, which we expect e.g. for biological
systems. Our results furthermore suggest that entanglement plays a role in the
heat exchange between molecular machines and environment. Experimental
simulation of our model with trapped ions is within reach of the current
state-of-the-art quantum technologies.Comment: Extended version, including supplementary information. 9 pages, 8
figure
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