Measures of entanglement for two-mode Gaussian states

KTH/Nordita/SU seminar in Theoretical Physics [before December 2013]

Tuesday 02 June 2009
from 13:15
to 14:15 at
FA32 (OBS!)

Speaker :

Paulina Marian (Bucharest)

Abstract :

For a long time Gaussian states of the quantum radiation field
are known to be of central importance in various areas of quantum
optics. In general, such quantum states play a conspicuous role for
those systems involving a quadratic bosonic Hamiltonian that generates
correlations between bosonic modes. They are achieved in condensed
matter, as well as in atomic ensembles such as trapped ions or
Bose-Einstein condensates. The Gaussian states of light are also largely
employed in quantum information processing with continuous variables.
Recent developments in the theory of quantum information focused on a
deeper understanding of the properties of entangled states. Several
measures of entanglement have been considered for mixed bipartite
states. Due to its operational meaning, one of the most promising is the
entanglement of formation (EF) defined as the minimal entanglement of
any ensemble of pure bipartite states realizing the given mixed state.
Our aproach to EF for Gaussian states is based on concepts currently
used in quantum optics, such as characteristic functions,
P-representativity and field superpositions. Combined with a more
abstract description of Gaussian states based on the properties of their
covariance matrices, we give an essentially physical approach to a
very complicated mathematical task, namely, the extremization problem of
EF. We then show that EF is consistent to another measure of
entanglement: the Bures distance between the given entangled Gaussian
state and the set of all separable states.