My friend and collaborator Kavan Modi had been posting on his blog his musings about Linear Assignments Maps, Correlations and Not-Completely Positive Maps. His original posts can be found here:
This was an experiment testing the possibilities of doing Open Science in theoretical research. It helped us to publicly discuss the issues, and after some discussion face to face, and private discussions using Google Wave (and the watexy robot for equations) we posted a paper in the arXiv!
Linear Assignment Maps for Correlated System-Environment States
An assignment map is a mathematical operator that describes initial system-environment states for open quantum systems. We reexamine the notion of assignments, introduced by Pechukas, and show the conditions assignments can account for correlations between the system and the environment, concluding that assignment maps can be made linear at the expense of positivity or consistency is more reasonable. We study the role of other conditions, such as consistency and positivity of the map, and show the effects of relaxing these. Finally, we establish a connection between the violation of positivity of linear assignments and the no-broadcasting theorem.
Very promptly, the paper was accepted for publication on Physical Review A, and should appear in the journal in a few weeks.
I’ll comment on my experiences of this clumsy and incomplete Open Science and remote collaboration attempt soon, hoping that the Open Science community will give me ideas of how to streamline this process.
When a reporter asked Asher [Asher Peres] if quantum teleportation could teleport the soul as well as the body, Asher answered, characteristically, “No, not the body, just the soul.”