Relating compatibility and divisibility of quantum channels

We connect two key concepts in quantum information: compatibility and divisibility of quantum channels. Two channels are compatible if they can be both obtained via marginalization from a third channel. A channel divides another channel if it reproduces its action by sequential composition with a third channel. (In)compatibility is of central importance for studying the difference between classical and quantum dynamics. The relevance of divisibility stands in its close relationship with the onset of Markovianity. We emphasize the simulability character of compatibility and divisibility, and, despite their structural difference, we find a set of channels -- self-degradable channels -- for which the two notions coincide. We also show that, for degradable channels, compatibility implies divisibility, and that, for anti-degradable channels, divisibility implies compatibility. These results motivate further research on these classes of channels and shed new light on the meaning of these two largely studied notions.Comment: Suggestions are welcome! =

Geometry of Entanglement Sudden Death: Explicit Examples

In open quantum systems, entanglement can vanish faster than coherence. This phenomenon is usually called sudden death of entanglement. In [M. O. Terra Cunha, New J. Phys. 9, 237 (2007)] a geometrical explanation was offered and a classification of all possible scenarios was given. Some classes were exemplified, but it was still an open question whether there were examples for the other ones. This was solved in [R.C. Drumond and M.O. Terra Cunha, arXiv:0809.4445v1]. Here we briefly review the problem, state our results in a precise way, discuss the generality of the approach, and add some speculative desirable generalizations.Comment: Contribution written to the Procceedings of 5th Vaxjo Conference on Foundations of Probability and Physic