I.F.T.
Almuerzo-Seminario
(Lunch seminar)
May 23th 2000, 15:00 p.m.
Quantum Information: separability and destillability of mixed states
Ignacio Cirac
(Innsbruck)
Most of the applications in the field of quantum information are based on
the existence of pure entangled states of several particles. However,
in practice, the states that one can prepare in the lab are statistical
mixtures of pure entangled states. Under certain conditions it is possible
to obtain the desired states starting from mixed states by using local
operations. This process is called distillation. One of the
fundamental problems in quantum information theory is to find out
necessary and sufficient conditions for a mixed state of several
particles to be distillable. This problem is directly related to the
one of non-separability: that is, the problem of finding the conditions
under which a mixed state of serveral particles can be prepared locally
(without any interactiong among them). Mathematically, this last is
connected to the existence of positive maps (which transform positive
operators into positive operators) which are not completely positive
(whose trivial extensions remain positive). Unfortunately, there exists
no way of constructing systematically positive maps, which implies
that there is no necessary and sufficient criterion to check separability.
In this talk I will present a method to construct in a systematic
way a certain class of (non--decomposable) positive maps.On the
other hand, I will give necessary and sufficient conditions for
separability for (moderate and) low rank density operators. I will also
connect these results with the problem of separability and destillability.
Finally, I will comment on the possibility of generalizing those
results to systems formed by more than two particles.
Where: Modulo C-XVI, 3rd floor,
Facultad de Ciencias U.A.M., C.U. Cantoblanco, 28049-Madrid
For more information about seminars at the I.F.T. e-mail
José Ramón Espinosa
or phone +34-91-397 4418.
Last modified: Wed Apr 12 10:10:08 CEST 2000