Geometry of quantum systems: density states and entanglement

Details Geometry of quantum systems: density states and entanglement Geometry of quantum systems: density states and entanglement

2005-07-18

arxiv.org/abs/math-ph/0507045v3

J.Phys. A38 (2005) 10217-10244

Physics

Mathematical Physics

Latex, 26 pages, minor corrections, published version

Scientific paper

10.1088/0305-4470/38/47/011

Various problems concerning the geometry of the space $u^*(\cH)$ of Hermitian operators on a Hilbert space $\cH$ are addressed. In particular, we study the canonical Poisson and Riemann-Jordan tensors and the corresponding foliations into K\"ahler submanifolds. It is also shown that the space $\cD(\cH)$ of density states on an $n$-dimensional Hilbert space $\cH$ is naturally a manifold stratified space with the stratification induced by the the rank of the state. Thus the space $\cD^k(\cH)$ of rank-$k$ states, $k=1,...,n$, is a smooth manifold of (real) dimension $2nk-k^2-1$ and this stratification is maximal in the sense that every smooth curve in $\cD(\cH)$, viewed as a subset of the dual $u^*(\cH)$ to the Lie algebra of the unitary group $U(\cH)$, at every point must be tangent to the strata $\cD^k(\cH)$ it crosses. For a quantum composite system, i.e. for a Hilbert space decomposition $\cH=\cH^1\ot\cH^2$, an abstract criterion of entanglement is proved.

Affiliated with

Also associated with

No associations

Rating

Geometry of quantum systems: density states and entanglement 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 Geometry of quantum systems: density states and entanglement, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometry of quantum systems: density states and entanglement will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-287863