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