EntanglementEntanglement is the property of quantum mechanics that there can be stronger correlations between subsystems than what is possible in any classical theory. It is important for many phenomena, and for such novel ideas as quantum teleportation, quantum cryptography and some quantum computer algorithms it is used as a resource.
In that respect it is important to quantify entanglement. Our project is to gain a better understanding of entanglement by understanding the geometry of entanglement.
Recent articlesSimplifying monotonicity conditions for entanglement; Michal Horodecki.
Previously Guifre Vidal has shown some necessary and sufficient inequalities that convex measures of entanglement has to satisfy to be monotone under Local Operations and Classical Communication. In this paper M. Horodecki use this result to derive two equalities that are necessary and sufficient conditions for monotonicity under LOCC. Again for convex measures, such as the minimal geometric distance to the set of separable states.
The new conditions looks to be easier to use in proving the monotonicity under LOCC for a given measure, and they are also much stronger since they are equalities. With the only inequality hidden in the convexity of the measure.
Review worksMeasures of entanglement in quantum mechanics; Geir Myhr.
A master thesis from Jan Myrheim's student Geir Myhr on entanglement measures
entanglement - criteria, measures, applications; Ingmar Weber.
Relativity of Pure States Entanglement;
Zyczkowski and Bengtsson.
Separability criteriaSeparability of mixed states: Necessary and sufficient conditions; Horodeckis
This is the article where they first prove that for the 2x2 and 2x3 case, ppt is sufficient for separability.
Separability criterion for density
matrices; Asher Peres.
Geometric distance as entanglement measureOn the geometry of entanglement; Verstraete et al.
Article with an algorithm for finding the closest PPT state.
witnesses for qubits and qutrits; Bertlmann et al.
Entanglement measures and the Hilbert-Schmidt
distance; Masanao Ozawa.
Monotone metrics on matrix spaces; Denes
Measures of entanglementConcentrating partial entanglement by local operations; Bennet et al.
In this article they show that one can take an ensemble of non-maximally entangled pairs of spin half particles and distill out a lesser amount of pairs of bells state pairs.
Computable measure of entanglement; Vidal
Mixed state entanglement and
distillation: Is there a "bound" entanglement in nature? ;
Monotonicity under LOCCAffine maps of density matrices; Thomas F. Jordan
A short article on complete positivity and unitary evolution.
AssortedA classical analogue of entanglement; Collins and Popescu
An article in which they find what sort of non-allowed devices are needed for having quantum correlations in a classical system.