4,157 research outputs found
Bound Entanglement and Teleportation
Recently M. Horodecki, P. Horodecki and R. Horodecki have introduced a set of
density matrices of two spin-1 particles from which it is not possible to
distill any maximally entangled states, even though the density matrices are
entangled. Thus these density matrices do not allow reliable teleportation.
However it might nevertheless be the case that these states can be used for
teleportation, not reliably, but still with fidelity greater than that which
may be achieved with a classical scheme. We show that, at least for some of
these density matrices, teleportation cannot be achieved with better than
classical fidelity.Comment: 3 pages, RevTe
Phase coexistence in a monolayer of active particles induced by Marangoni flows
Thermally or chemically active colloids generate thermodynamic gradients in
the solution in which they are immersed and thereby induce hydrodynamic flows
that affect their dynamical evolution. Here we study a mean-field model for the
many-body dynamics of a monolayer of active particles located at a fluid-fluid
interface. In this case, the activity of the particles creates long-ranged
Marangoni flows due to the response of the interface, which compete with the
direct interaction between the particles. For the most interesting case of a
soft repulsion that models the electrostatic or magnetic interparticle
forces, we show that an "onion-like" density distribution will develop within
the monolayer. For a sufficiently large average density, two-dimensional phase
transitions (freezing from liquid to hexatic, and melting from solid to
hexatic) should be observable in a radially stratified structure. Furthermore,
the analysis allows us to conclude that, while the activity may be too weak to
allow direct detection of such induced Marangoni flows, it is relevant as a
collective effect in the emergence of the experimentally observable spatial
structure of phase coexistences noted above. Finally, the relevance of these
results for potential experimental realizations is critically discussed.Comment: 11 page
Shy and Fixed-Distance Couplings of Brownian Motions on Manifolds
In this paper we introduce three Markovian couplings of Brownian motions on
smooth Riemannian manifolds without boundary which sit at the crossroad of two
concepts. The first concept is the one of shy coupling put forward in
\cite{Burdzy-Benjamini} and the second concept is the lower bound on the Ricci
curvature and the connection with couplings made in \cite{ReSt}.
The first construction is the shy coupling, the second one is a
fixed-distance coupling and the third is a coupling in which the distance
between the processes is a deterministic exponential function of time.
The result proved here is that an arbitrary Riemannian manifold satisfying
some technical conditions supports shy couplings. If in addition, the Ricci
curvature is non-negative, there exist fixed-distance couplings. Furthermore,
if the Ricci curvature is bounded below by a positive constant, then there
exists a coupling of Brownian motions for which the distance between the
processes is a decreasing exponential function of time. The constructions use
the intrinsic geometry, and relies on an extension of the notion of frames
which plays an important role for even dimensional manifolds.
In fact, we provide a wider class of couplings in which the distance function
is deterministic in Theorem \ref{t:100} and Corollary~\ref{Cor:9}.
As an application of the fixed-distance coupling we derive a maximum
principle for the gradient of harmonic functions on manifolds with non-negative
Ricci curvature.
As far as we are aware of, these constructions are new, though the existence
of shy couplings on manifolds is suggested by Kendall in \cite{Kendall}.Comment: This version is a refinement expansion and simplification of the
previous versio
Purifying noisy entanglement requires collective measurements
Known entanglement purification protocols for mixed states use collective
measurements on several copies of the state in order to increase the
entanglement of some of them. We address the question of whether it is possible
to purify the entanglement of a state by processing each copy separately. While
this is possible for pure states, we show that this is impossible, in general,
for mixed states. The importance of this result both conceptually and for
experimental realization of purification is discussed. We also give explicit
invariants of an entangled state of two qubits under local actions and
classical communication.Comment: 5 pages, Late
Non-local properties of multi-particle density matrices
As far as entanglement is concerned, two density matrices of particles
are equivalent if they are on the same orbit of the group of local unitary
transformations, (where the Hilbert space of
particle has dimension ). We show that for greater than or equal
to two, the number of independent parameters needed to specify an -particle
density matrix up to equivalence is . For
spin- particles we also show how to characterise generic
orbits, both by giving an explicit parametrisation of the orbits and by finding
a finite set of polynomial invariants which separate the orbits.Comment: 13 pages RevTe
Diffusive spreading and mixing of fluid monolayers
The use of ultra-thin, i.e., monolayer films plays an important role for the
emerging field of nano-fluidics. Since the dynamics of such films is governed
by the interplay between substrate-fluid and fluid-fluid interactions, the
transport of matter in nanoscale devices may be eventually efficiently
controlled by substrate engineering. For such films, the dynamics is expected
to be captured by two-dimensional lattice-gas models with interacting
particles. Using a lattice gas model and the non-linear diffusion equation
derived from the microscopic dynamics in the continuum limit, we study two
problems of relevance in the context of nano-fluidics. The first one is the
case in which along the spreading direction of a monolayer a mesoscopic-sized
obstacle is present, with a particular focus on the relaxation of the fluid
density profile upon encountering and passing the obstacle. The second one is
the mixing of two monolayers of different particle species which spread side by
side following the merger of two chemical lanes, here defined as domains of
high affinity for fluid adsorption surrounded by domains of low affinity for
fluid adsorption.Comment: 12 pages, 3 figure
Active colloids at fluid interfaces
If an active Janus particle is trapped at the interface between a liquid and
a fluid, its self-propelled motion along the interface is affected by a net
torque on the particle due to the viscosity contrast between the two adjacent
fluid phases. For a simple model of an active, spherical Janus colloid we
analyze the conditions under which translation occurs along the interface and
we provide estimates of the corresponding persistence length. We show that
under certain conditions the persistence length of such a particle is
significantly larger than the corresponding one in the bulk liquid, which is in
line with the trends observed in recent experimental studies
Bell inequalities for arbitrarily high dimensional systems
We develop a novel approach to Bell inequalities based on a constraint that
the correlations exhibited by local realistic theories must satisfy. This is
used to construct a family of Bell inequalities for bipartite quantum systems
of arbitrarily high dimensionality which are strongly resistant to noise. In
particular our work gives an analytic description of numerical results of D.
Kaszlikowski, P. Gnacinski, M. Zukowski, W. Miklaszewski, A. Zeilinger, Phys.
Rev. Lett. {\bf 85}, 4418 (2000) and T. Durt, D. Kaszlikowski, M. Zukowski,
quant-ph/0101084, and generalises them to arbitrarily high dimensionality.Comment: 6 pages, late
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