SLOCC. Let us recall that, all in all, no practical criterion is known so far that determines whether a generic transformation can be implemented by means of LOCC. However, we can think of any local protocol as a series of rounds of operations, where in each round a given party manipulates locally its subsystem and communicates classically the result of its operation (if it included a measurement) to the rest of parties. Subsequent operations can be made dependent on previous results and the protocol splits into several branches. This picture is useful because for our purposes we need only focus on one of these branches. Suppose that state ${\mbox{$| \psi \rangle$}}$ can be locally converted into state ${\mbox{$| \phi \rangle$}}$ with non-zero probability. This means that at least one branch of the protocol does the job. Since we are concerned only with pure states we can always characterize mathematically this branch as an operator which factors out as the tensor product of a local operator for each party. For instance, in a three-qubit case we would have that ${\mbox{$| \psi \rangle$}}$ can be locally converted into ${\mbox{$| \phi \rangle$}}$ with some finite probability iff an operator $A\otimes B \otimes C$ 