Generalizations of entanglement based on coherent states and convex sets

Details Generalizations of entanglement based on coherent states and convex sets Generalizations of entanglement based on coherent states and convex sets

2002-07-26

arxiv.org/abs/quant-ph/0207149v1

Physics

Quantum Physics

37 pages

Scientific paper

10.1103/PhysRevA.68.032308

Unentangled pure states on a bipartite system are exactly the coherent states with respect to the group of local transformations. What aspects of the study of entanglement are applicable to generalized coherent states? Conversely, what can be learned about entanglement from the well-studied theory of coherent states? With these questions in mind, we characterize unentangled pure states as extremal states when considered as linear functionals on the local Lie algebra. As a result, a relativized notion of purity emerges, showing that there is a close relationship between purity, coherence and (non-)entanglement. To a large extent, these concepts can be defined and studied in the even more general setting of convex cones of states. Based on the idea that entanglement is relative, we suggest considering these notions in the context of partially ordered families of Lie algebras or convex cones, such as those that arise naturally for multipartite systems. The study of entanglement includes notions of local operations and, for information-theoretic purposes, entanglement measures and ways of scaling systems to enable asymptotic developments. We propose ways in which these may be generalized to the Lie-algebraic setting, and to a lesser extent to the convex-cones setting. One of our original motivations for this program is to understand the role of entanglement-like concepts in condensed matter. We discuss how our work provides tools for analyzing the correlations involved in quantum phase transitions and other aspects of condensed-matter systems.

Affiliated with

Also associated with

No associations

Rating

Generalizations of entanglement based on coherent states and convex sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalizations of entanglement based on coherent states and convex sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalizations of entanglement based on coherent states and convex sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-111312