Geometry of entangled states - art. no. 032307

Geometric properties of the set of quantum entangled states are investigate d. We propose an explicit method to compute the dimension of local orbits f or any mixed state of the general K x M problem and characterize the set of effectively different states (which cannot be related by local transformat ions). Thus, we generalize earlier results obtained for the simplest 2 x 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 whic h all globally equivalent states are separable.