Physics – Quantum Physics
Scientific paper
2012-01-05
Physics
Quantum Physics
5 pages, an open question is formulated, comments are welcome
Scientific paper
It is well known that the von Neumann entropy is continuous on a subset of quantum states with bounded energy provided the Hamiltonian $H$ of the system satisfies the condition $\Tr\exp(-cH)<+\infty$ for any $c>0$. In this note we consider the following conjecture: every closed convex subset of quantum states, on which the von Neumann entropy is continuous, consists of states with bounded energy with respect to a particular Hamiltonian $H$ satisfying the above condition. It is shown that the classical analog of this conjecture is valid (i.e. it is valid for the Shannon entropy). It is also shown that this conjecture holds for some types of subsets consisting of non-commuting states, but its validity for all subsets of quantum states remains an open question.
No associations
LandOfFree
On a conjectured property of the von Neumann entropy valid in the commutative case 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 a conjectured property of the von Neumann entropy valid in the commutative case, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a conjectured property of the von Neumann entropy valid in the commutative case will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-609414