Thread #59418 Message #1412602

Posted By: Rapparee

16-Feb-05 - 09:25 PM

Thread Name: BS: The Mother of all BS threads

Subject: RE: BS: The Mother of all BS threads

Bee-dubya, I agree with you and I gift you with my agreement.

Layah, the problem that people experience with your name is called "entanglement" and GUBS says this:

The entanglement of formation is one of the standard measures of entanglement. It is defined, for any density operator \rho on a bipartite system, as

E F(\rho)= inf { \sumi ri S(\rhoi|A) \Big|\, \sumi ri \rhoi = \rho },

where S(.) denotes the von Neumann entropy and \rho|A denotes the restriction of a density operator \rho to the "Alice'' subsystem (partial trace over the other subsystem), the \rhoi are density operators and the ri are positive, adding up to one. Since S is concave, the infimum is attained at a convex decomposition of \rho into pure states, and the definition is often given as this restricted infimum.

Consider now a pair \rho(i), i=1,2 of bipartite density operators, and their tensor product \rho=\rho(1)\otimes\rho(2), which lives on a tensor product of four Hilbert spaces, but can be considered as a bipartite state when the two Alice subsepaces and the two Bob subspaces are grouped together. Then it is easy to show (by plugging the tensor product of the optimal decompositions of the factors into the variational expression and using the additivity of the entropy) that E F(\rho) <= E F(\rho(1)) + E F(\rho(2)).

I'm certain that you will agree that that clears your name.