Geometry of entangled states

Abstract

Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general $K\ifmmode\times\else\texttimes\fi{}M$ problem and characterize the set of effectively different states (which cannot be related by local transformations). Thus, we generalize earlier results obtained for the simplest $2\ifmmode\times\else\texttimes\fi{}2$ system, which lead to a stratification of the six-dimensional set of $N=4$ pure states. We define the concept of absolutely separable states, for which all globally equivalent states are separable.