Measures and dynamics of entangled states

In the first part of the present thesis, we derive a theory for
quantifying entanglement of mixed bipartite quantum states. We
derive upper and lower bounds for the concurrence of quantum states
in arbitrary finite dimensions, such as to confine its actual value
to a finite interval. We test these estimates for various sets of
states with very satisfactory results. In particular, our lower
bound detects entangled states with positive partial transpose. In
view of the specific requirements of laboratory experiments, we
derive an approximate expression for the concurrence of almost pure
- i.e. weakly mixed - states. Comparison of this quasi-pure
approximation with the above upper and lower bounds shows that its
range of validity even comprises states with relatively large
mixing. Finally, we propose a generalised concurrence for
multipartite mixed states. For its quantitative characterisation,
we can use the same strategies as in our treatment of bipartite
systems. These novel techniques for a quantitative description of
the entanglement of mixed states allow to monitor the production
and the decay of entanglement under coherent and incoherent forcing
- as we show by applying our theory to a realistic scenario of ion
trap experiments. In the second part of the thesis, we introduce
suitably defined quasi probability representations such as to
quantify the entanglement of pure bipartite states, with an
immediate generalisation for pure states of multipartite systems.
It is shown that the statistical moments as well as various
entropies of these representations - characterising their
localisation properties - are non-increasing under local operations
and classical communication, hence that they are proper
entanglement monotones.