7,416 research outputs found
The distillability problem revisited
An important open problem in quantum information theory is the question of
the existence of NPT bound entanglement. In the past years, little progress has
been made, mainly because of the lack of mathematical tools to address the
problem. (i) In an attempt to overcome this, we show how the distillability
problem can be reformulated as a special instance of the separability problem,
for which a large number of tools and techniques are available. (ii) Building
up to this we also show how the problem can be formulated as a Schmidt number
problem. (iii) A numerical method for detecting distillability is presented and
strong evidence is given that all 1-copy undistillable Werner states are also
4-copy undistillable. (iv) The same method is used to estimate the volume of
distillable states, and the results suggest that bound entanglement is
primarily a phenomenon found in low dimensional quantum systems. (v) Finally, a
set of one parameter states is presented which we conjecture to exhibit all
forms of distillability.Comment: Several corrections, main results unchange
Global Orbit Patterns for One Dimensional Dynamical Systems
In this article, we study the behaviour of discrete one-dimensional dynamical
systems associated to functions on finite sets. We formalise the global orbit
pattern formed by all the periodic orbits (gop) as the ordered set of periods
when the initial value thumbs the finite set in the increasing order. We are
able to predict, using closed formulas, the number of gop for the set
of all the functions on . We also explore by computer
experiments special subsets of in which interesting patterns of
gop are found.Comment: 33 pages, 1 figur
Frequency-dependent streaming potentials: a review
The interpretation of seismoelectric observations involves the dynamic
electrokinetic coupling, which is related to the streaming potential
coefficient. We describe the different models of the frequency-dependent
streaming potential, mainly the Packard's and the Pride's model. We compare the
transition frequency separating low-frequency viscous flow and high-frequency
inertial flow, for dynamic permeability and dynamic streaming potential. We
show that the transition frequency, on a various collection of samples for
which both formation factor and permeability are measured, is predicted to
depend on the permeability as inversely proportional to the permeability. We
review the experimental setups built to be able to perform dynamic
measurements. And we present some measurements and calculations of the dynamic
streaming potential
On independent permutation separability criteria
Recently P. Wocjan and M. Horodecki [quant-ph/0503129] gave a
characterization of combinatorially independent permutation separability
criteria. Combinatorial independence is a necessary condition for permutations
to yield truly independent criteria meaning that that no criterion is strictly
stronger that any other. In this paper we observe that some of these criteria
are still dependent and analyze why these dependencies occur. To remove them we
introduce an improved necessary condition and give a complete classification of
the remaining permutations. We conjecture that the remaining class of criteria
only contains truly independent permutation separability criteria. Our
conjecture is based on the proof that for two, three and four parties all these
criteria are truly independent and on numerical verification of their
independence for up to 8 parties. It was commonly believed that for three
parties there were 9 independent criteria, here we prove that there are exactly
6 independent criteria for three parties and 22 for four parties.Comment: Revtex4, 7 pages, minor correction
The disentangling power of unitaries
We define the disentangling power of a unitary operator in a similar way as the entangling power defined by Zanardi et al. [P. Zanardi, C. Zalka, L. Faoro, Phys. Rev. A 62 (2000) 030301(R), quant-ph/0005031]. A general formula is derived and it is shown that both quantities are directly proportional. All results concerning the entangling power can simply be translated into similar statements for the disentangling power. In particular, the disentangling power is maximal for certain permutations derived from orthogonal Latin squares. These permutations can therefore be interpreted as those that distort entanglement in a maximal way
Bootstrap Methods for Inference in a SUR model with Autocorrelated Disturbances
Although the Parks (1967) estimator for a SUR model with AR disturbances is efficient both asymptotically and in small samples, Kmenta and Gilbert (1970) and more recently Beck and Katz (1995) note that estimated standard errors tend to be biased downward as compared with the true variability of the estimates. This bias leads to tests that show over-rejection and to confidence intervals that are too small. We suggest bootstrapping the tests to correct this inference problem. After illustrating the over rejection associated with the estimated asymptotic standard errors, we develop a bootstrap approach to inference for this model, illustrate its use, and show using Monte Carlo methods that the bootstrap gives rejection probabilities close to the nominal level chosen by the researcher.
Set-based Multiobjective Fitness Landscapes: A Preliminary Study
Fitness landscape analysis aims to understand the geometry of a given
optimization problem in order to design more efficient search algorithms.
However, there is a very little knowledge on the landscape of multiobjective
problems. In this work, following a recent proposal by Zitzler et al. (2010),
we consider multiobjective optimization as a set problem. Then, we give a
general definition of set-based multiobjective fitness landscapes. An
experimental set-based fitness landscape analysis is conducted on the
multiobjective NK-landscapes with objective correlation. The aim is to adapt
and to enhance the comprehensive design of set-based multiobjective search
approaches, motivated by an a priori analysis of the corresponding set problem
properties
On two-distillable Werner states
We consider bipartite mixed states in a quantum system. We say
that is PPT if its partial transpose is positive
semidefinite, and otherwise is NPT. The well-known Werner states are
divided into three types: (a) the separable states (the same as the PPT
states); (b) the one-distillable states (necessarily NPT); and (c) the NPT
states which are not one-distillable. We give several different formulations
and provide further evidence for validity of the conjecture that the Werner
states of type (c) are not two-distillable.Comment: 19 pages, expanded version containing new result
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