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Lamata et al. use an inductive approach to classify the entangled pure statesof four qubits under stochastic local operations and classical communication(SLOCC) [PRA 75(2), 022318 (2007)]. The inductive method yields a priori tendifferent entanglement superclasses, of which they discard three as empty. Oneof the remaining superclasses is split in two, resulting in eight superclassesof genuine four-qubit entanglement.  Here, we show that two of the three discarded superclasses are in factnon-empty and should have been retained. We give explicit expressions for thecanonical states for those superclasses, up to SLOCC and qubit permutations.Furthermore, we confirm that the third discarded superclass is indeed empty,yielding a total of ten superclasses of genuine four-qubit entanglement underthe inductive classification scheme.

The inductive entanglement classification yields ten rather than eight classes of four-qubit entangled states