2,166 research outputs found
Variational Characterisations of Separability and Entanglement of Formation
In this paper we develop a mathematical framework for the characterisation of
separability and entanglement of formation (EoF) of general bipartite states.
These characterisations are of the variational kind, meaning that separability
and EoF are given in terms of a function which is to be minimized over the
manifold of unitary matrices. A major benefit of such a characterisation is
that it directly leads to a numerical procedure for calculating EoF. We present
an efficient minimisation algorithm and an apply it to the bound entangled 3X3
Horodecki states; we show that their EoF is very low and that their distance to
the set of separable states is also very low. Within the same variational
framework we rephrase the results by Wootters (W. Wootters, Phys. Rev. Lett.
80, 2245 (1998)) on EoF for 2X2 states and present progress in generalising
these results to higher dimensional systems.Comment: 11 pages RevTeX, 4 figure
On the geometry of entangled states
The basic question that is addressed in this paper is finding the closest
separable state for a given entangled state, measured with the Hilbert Schmidt
distance. While this problem is in general very hard, we show that the
following strongly related problem can be solved: find the Hilbert Schmidt
distance of an entangled state to the set of all partially transposed states.
We prove that this latter distance can be expressed as a function of the
negative eigenvalues of the partial transpose of the entangled state, and show
how it is related to the distance of a state to the set of positive partially
transposed states (PPT-states). We illustrate this by calculating the closest
biseparable state to the W-state, and give a simple and very general proof for
the fact that the set of W-type states is not of measure zero. Next we show
that all surfaces with states whose partial transposes have constant minimal
negative eigenvalue are similar to the boundary of PPT states. We illustrate
this with some examples on bipartite qubit states, where contours of constant
negativity are plotted on two-dimensional intersections of the complete state
space.Comment: submitted to Journal of Modern Optic
EnsembleSVM: A Library for Ensemble Learning Using Support Vector Machines
EnsembleSVM is a free software package containing efficient routines to
perform ensemble learning with support vector machine (SVM) base models. It
currently offers ensemble methods based on binary SVM models. Our
implementation avoids duplicate storage and evaluation of support vectors which
are shared between constituent models. Experimental results show that using
ensemble approaches can drastically reduce training complexity while
maintaining high predictive accuracy. The EnsembleSVM software package is
freely available online at http://esat.kuleuven.be/stadius/ensemblesvm.Comment: 5 pages, 1 tabl
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