1208.0557 (Adam Sawicki et al.)

Critical sets of the total variance of state detect all SLOCC
entanglement classes    [PDF]

Adam Sawicki, Michał Oszmaniec, Marek Kuś

We present a general algorithm for finding all classes of pure multiparticle states equivalent under Stochastic Local Operations and Classsical Communication (SLOCC). We parametrize all SLOCC classes by the critical sets of the total variance function. Our method works for arbitrary systems of distinguishable and indistinguishable particles. We also discuss the Morse indices of critical points which have the interpretation of the number of independent non-local perturbations increasing the variance and hence entanglement of a state. We illustrate our method by two examples.

View original: http://arxiv.org/abs/1208.0557