14 research outputs found
Kochen-Specker set with seven contexts
The Kochen-Specker (KS) theorem is a central result in quantum theory and has
applications in quantum information. Its proof requires several yes-no tests
that can be grouped in contexts or subsets of jointly measurable tests.
Arguably, the best measure of simplicity of a KS set is the number of contexts.
The smaller this number is, the smaller the number of experiments needed to
reveal the conflict between quantum theory and noncontextual theories and to
get a quantum vs classical outperformance. The original KS set had 132
contexts. Here we introduce a KS set with seven contexts and prove that this is
the simplest KS set that admits a symmetric parity proof.Comment: REVTeX4, 7 pages, 1 figur
Concurrence in arbitrary dimensions
We argue that a complete characterisation of quantum correlations in
bipartite systems of many dimensions may require a quantity which, even for
pure states, does not reduce to a single number. Subsequently, we introduce
multi-dimensional generalizations of concurrence and find evidence that they
may provide useful tools for the analysis of quantum correlations in mixed
bipartite states. We also introudce {\it biconcurrence} that leads to a
necessary and sufficient condition for separability.Comment: RevTeX 7 page
CHSH type Bell inequalities involving a party with two or three local binary settings
We construct a simple algorithm to generate any CHSH type Bell inequality
involving a party with two local binary measurements from two CHSH type
inequalities without this party. The algorithm readily generalizes to
situations, where the additional observer uses three measurement settings.
There, each inequality involving the additional party is constructed from three
inequalities with this party excluded. With this generalization at hand, we
construct and analyze new symmetric inequalities for four observers and three
experimental settings per observer.Comment: 8 pages, no figur
Extending Bell inequalities to more parties
We describe a method of extending Bell inequalities from to parties
and formulate sufficient conditions for our method to produce tight
inequalities from tight inequalities. The method is non trivial in the sense
that the inequalities produced by it, when applied to entangled quantum states
may be violated stronger than the original inequalities. In other words, the
method is capable of generating inequalities which are more powerfull
indicators of non-classical correlations than the original inequalities.Comment: 8 pages, no figur