SLOCC classification for nine families of four-qubits

Abstract

In Phys. Rev. A 62, 062314 (2000), D\"{u}r, Vidal and Cirac indicated that there are infinitely many SLOCC classes for four qubits. Verstraete, Dehaene, and Verschelde in Phys. Rev. A 65, 052112 (2002) proposed nine families of states corresponding to nine different ways of entangling four qubits. In Phys. Rev. A 75, 022318 (2007), Lamata et al. reported that there are eight true SLOCC entanglement classes of four qubits up to permutations of the qubits. In this paper, we investigate SLOCC classification of the nine families proposed by Verstraete, Dehaene and Verschelde, and distinguish 49 true SLOCC entanglement classes from them.