Physics – Quantum Physics
Scientific paper
2004-06-03
J.Math.Phys. 45 (2004), 4035-4041
Physics
Quantum Physics
6 pages, to appear in J.Math.Phys
Scientific paper
10.1063/1.1776642
We study the convex set of all bipartite quantum states with fixed marginal states. The extremal states in this set have recently been characterized by Parthasarathy [Ann. Henri Poincar\'e (to appear), quant-ph/0307182, [1]]. Here we present an alternative necessary and sufficient condition for a state with given marginals to be extremal. Our approach is based on a canonical duality between bipartite states and a certain class of completely positive maps and has the advantage that it is easier to check and to construct explicit examples of extremal states. In dimension 2 x 2 we give a simple new proof for the fact that all extremal states with maximally mixed marginals are precisely the projectors onto maximally entangled wave functions. We also prove that in higher dimension this does not hold and construct an explicit example of an extremal state with maximally mixed marginals in dimension 3 x 3 that is not maximally entangled. Generalizations of this result to higher dimensions are also discussed.
Rudolph Oliver
No associations
LandOfFree
On extremal quantum states of composite systems with fixed marginals 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 On extremal quantum states of composite systems with fixed marginals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On extremal quantum states of composite systems with fixed marginals will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-618472