818 research outputs found
Some Properties of the Computable Cross Norm Criterion for Separability
The computable cross norm (CCN) criterion is a new powerful analytical and
computable separability criterion for bipartite quantum states, that is also
known to systematically detect bound entanglement. In certain aspects this
criterion complements the well-known Peres positive partial transpose (PPT)
criterion. In the present paper we study important analytical properties of the
CCN criterion. We show that in contrast to the PPT criterion it is not
sufficient in dimension 2 x 2. In higher dimensions we prove theorems
connecting the fidelity of a quantum state with the CCN criterion. We also
analyze the behaviour of the CCN criterion under local operations and identify
the operations that leave it invariant. It turns out that the CCN criterion is
in general not invariant under local operations.Comment: 7 pages; accepted by Physical Review A; error in Appendix B correcte
One-and-a-half quantum de Finetti theorems
We prove a new kind of quantum de Finetti theorem for representations of the
unitary group U(d). Consider a pure state that lies in the irreducible
representation U_{mu+nu} for Young diagrams mu and nu. U_{mu+nu} is contained
in the tensor product of U_mu and U_nu; let xi be the state obtained by tracing
out U_nu. We show that xi is close to a convex combination of states Uv, where
U is in U(d) and v is the highest weight vector in U_mu. When U_{mu+nu} is the
symmetric representation, this yields the conventional quantum de Finetti
theorem for symmetric states, and our method of proof gives near-optimal bounds
for the approximation of xi by a convex combination of product states. For the
class of symmetric Werner states, we give a second de Finetti-style theorem
(our 'half' theorem); the de Finetti-approximation in this case takes a
particularly simple form, involving only product states with a fixed spectrum.
Our proof uses purely group theoretic methods, and makes a link with the
shifted Schur functions. It also provides some useful examples, and gives some
insight into the structure of the set of convex combinations of product states.Comment: 14 pages, 3 figures, v4: minor additions (including figures),
published versio
Interaction-free generation of entanglement
In this paper, we study how to generate entanglement by interaction-free
measurement. Using Kwiat et al.'s interferometer, we construct a two-qubit
quantum gate that changes a particle's trajectory according to the other
particle's trajectory. We propose methods for generating the Bell state from an
electron and a positron and from a pair of photons by this gate. We also show
that using this gate, we can carry out the Bell measurement with the
probability of 3/4 at the maximum and execute a controlled-NOT operation by the
method proposed by Gottesman and Chuang with the probability of 9/16 at the
maximum. We estimate the success probability for generating the Bell state by
our procedure under imperfect interaction.Comment: 18 pages, Latex2e, 11 eps figures, v2: minor corrections and one
reference added, v3: a minor correctio
A general T-matrix approach applied to two-body and three-body problems in cold atomic gases
We propose a systematic T-matrix approach to solve few-body problems with
s-wave contact interactions in ultracold atomic gases. The problem is generally
reduced to a matrix equation expanded by a set of orthogonal molecular states,
describing external center-of-mass motions of pairs of interacting particles;
while each matrix element is guaranteed to be finite by a proper
renormalization for internal relative motions. This approach is able to
incorporate various scattering problems and the calculations of related
physical quantities in a single framework, and also provides a physically
transparent way to understand the mechanism of resonance scattering. For
applications, we study two-body effective scattering in 2D-3D mixed dimensions,
where the resonance position and width are determined with high precision from
only a few number of matrix elements. We also study three fermions in a
(rotating) harmonic trap, where exotic scattering properties in terms of mass
ratios and angular momenta are uniquely identified in the framework of
T-matrix.Comment: 14 pages, 4 figure
Faithful Squashed Entanglement
Squashed entanglement is a measure for the entanglement of bipartite quantum
states. In this paper we present a lower bound for squashed entanglement in
terms of a distance to the set of separable states. This implies that squashed
entanglement is faithful, that is, strictly positive if and only if the state
is entangled. We derive the bound on squashed entanglement from a bound on
quantum conditional mutual information, which is used to define squashed
entanglement and corresponds to the amount by which strong subadditivity of von
Neumann entropy fails to be saturated. Our result therefore sheds light on the
structure of states that almost satisfy strong subadditivity with equality. The
proof is based on two recent results from quantum information theory: the
operational interpretation of the quantum mutual information as the optimal
rate for state redistribution and the interpretation of the regularised
relative entropy of entanglement as an error exponent in hypothesis testing.
The distance to the set of separable states is measured by the one-way LOCC
norm, an operationally-motivated norm giving the optimal probability of
distinguishing two bipartite quantum states, each shared by two parties, using
any protocol formed by local quantum operations and one-directional classical
communication between the parties. A similar result for the Frobenius or
Euclidean norm follows immediately. The result has two applications in
complexity theory. The first is a quasipolynomial-time algorithm solving the
weak membership problem for the set of separable states in one-way LOCC or
Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show
that multiple provers are not more powerful than a single prover when the
verifier is restricted to one-way LOCC operations thereby providing a new
characterisation of the complexity class QMA.Comment: 24 pages, 1 figure, 1 table. Due to an error in the published
version, claims have been weakened from the LOCC norm to the one-way LOCC
nor
Variability in oxidative degradation of charcoal: influence of production variables and environmental exposure
<p>Charcoal is a key component of the Black Carbon (BC) continuum, where BC is characterized as a recalcitrant, fire-derived, polyaromatic material. Charcoal is an important source of palaeoenvironmental data, and of great interest as a potential carbon sink, due to its high apparent environmental stability. However, at least some forms of charcoal are clearly susceptible to environmental alteration and degradation over relatively short timescales. Although these processes have importance for the role of charcoal in global biogeochemistry, they remain poorly understood.</p>
<p>Here we present results of an investigation into the susceptibility of a range of charcoal samples to oxidative degradation in acidified potassium dichromate. The study examines both freshly-produced charcoal, and charcoal exposed to environmental conditions for up to 50,000 years. We compare the proportion of carbon present in different forms between the samples, specifically with respect to the relative chemical resistance of these forms. This was undertaken in order to improve understanding of the post-depositional diagenetic changes affecting charcoal within environmental deposits.</p>
<p>A wide range in chemical compositions are apparent both within and between the sample groups. In freshly-produced charcoal, material produced at 300 °C contains carbon with more labile forms than charcoal produced at ≥400 °C, signifying a key chemical change over the 300–400 °C temperature range. Charcoal exposed to environmental depositional conditions is frequently composed of a highly carboxylated aromatic structure and contains a range of carbon fractions of varying oxidative resistance. These findings suggest that a significant number of the environmental charcoals have undergone post-depositional diagenetic alteration. Further, the data highlight the potential for the use of controlled progressive oxidative degradation as a method to characterize chemical differences between individual charcoal samples.</p>
Spinodal Decomposition in a Binary Polymer Mixture: Dynamic Self Consistent Field Theory and Monte Carlo Simulations
We investigate how the dynamics of a single chain influences the kinetics of
early stage phase separation in a symmetric binary polymer mixture. We consider
quenches from the disordered phase into the region of spinodal instability. On
a mean field level we approach this problem with two methods: a dynamical
extension of the self consistent field theory for Gaussian chains, with the
density variables evolving in time, and the method of the external potential
dynamics where the effective external fields are propagated in time. Different
wave vector dependencies of the kinetic coefficient are taken into account.
These early stages of spinodal decomposition are also studied through Monte
Carlo simulations employing the bond fluctuation model that maps the chains --
in our case with 64 effective segments -- on a coarse grained lattice. The
results obtained through self consistent field calculations and Monte Carlo
simulations can be compared because the time, length, and temperature scales
are mapped onto each other through the diffusion constant, the chain extension,
and the energy of mixing. The quantitative comparison of the relaxation rate of
the global structure factor shows that a kinetic coefficient according to the
Rouse model gives a much better agreement than a local, i.e. wave vector
independent, kinetic factor. Including fluctuations in the self consistent
field calculations leads to a shorter time span of spinodal behaviour and a
reduction of the relaxation rate for smaller wave vectors and prevents the
relaxation rate from becoming negative for larger values of the wave vector.
This is also in agreement with the simulation results.Comment: Phys.Rev.E in prin
Orbital-selective Mott transitions: Heavy fermions and beyond
Quantum phase transitions in metals are often accompanied by violations of
Fermi liquid behavior in the quantum critical regime. Particularly fascinating
are transitions beyond the Landau-Ginzburg-Wilson concept of a local order
parameter. The breakdown of the Kondo effect in heavy-fermion metals
constitutes a prime example of such a transition. Here, the strongly correlated
f electrons become localized and disappear from the Fermi surface, implying
that the transition is equivalent to an orbital-selective Mott transition, as
has been discussed for multi-band transition-metal oxides. In this article,
available theoretical descriptions for orbital-selective Mott transitions will
be reviewed, with an emphasis on conceptual aspects like the distinction
between different low-temperature phases and the structure of the global phase
diagram. Selected results for quantum critical properties will be listed as
well. Finally, a brief overview is given on experiments which have been
interpreted in terms of orbital-selective Mott physics.Comment: 29 pages, 4 figs, mini-review prepared for a special issue of JLT
Rings and bars: unmasking secular evolution of galaxies
Secular evolution gradually shapes galaxies by internal processes, in
contrast to early cosmological evolution which is more rapid. An important
driver of secular evolution is the flow of gas from the disk into the central
regions, often under the influence of a bar. In this paper, we review several
new observational results on bars and nuclear rings in galaxies. They show that
these components are intimately linked to each other, and to the properties of
their host galaxy. We briefly discuss how upcoming observations, e.g., imaging
from the Spitzer Survey of Stellar Structure in Galaxies (S4G), will lead to
significant further advances in this area of research.Comment: Invited review at "Galaxies and their Masks", celebrating Ken
Freeman's 70-th birthday, Sossusvlei, Namibia, April 2010. To be published by
Springer, New York, editors D.L. Block, K.C. Freeman, & I. Puerari; minor
change
Gravitational Lensing by Black Holes
We review the theoretical aspects of gravitational lensing by black holes,
and discuss the perspectives for realistic observations. We will first treat
lensing by spherically symmetric black holes, in which the formation of
infinite sequences of higher order images emerges in the clearest way. We will
then consider the effects of the spin of the black hole, with the formation of
giant higher order caustics and multiple images. Finally, we will consider the
perspectives for observations of black hole lensing, from the detection of
secondary images of stellar sources and spots on the accretion disk to the
interpretation of iron K-lines and direct imaging of the shadow of the black
hole.Comment: Invited article for the GRG special issue on lensing (P. Jetzer, Y.
Mellier and V. Perlick Eds.). 31 pages, 12 figure
- …