Comment: Inductive entanglement classification of four qubits under stochastic local operation and classical communication

Abstract

L. Lamata et al. have presented an entanglement classification of four qubits under stochastic local operation and classical communication (SLOCC) based on inductive approach [Phys. Rev. A \textbf{75}, 022318 (2007)]. While it works well for three qubits, we show that some of the families for four qubits have overlaps and hence this approach is not valid for entanglement classification of four or more qubits under SLOCC.

References in corpus (6)

• Three qubits can be entangled in two inequivalent ways
• Exact and Asymptotic Measures of Multipartite Pure State Entanglement
• Inductive Entanglement Classification of Four Qubits under SLOCC
• Inductive classification of multipartite entanglement under SLOCC
• Entanglement classification with matrix product states
• The inductive entanglement classification yields ten rather than eight classes of four-qubit entangled states

Cited by in corpus (9)

• Entanglement in highly symmetric multipartite quantum states
• Stochastic Local Operations with Classical Communication of Absolutely Maximally Entangled States
• Fine-Structure Classification of Multiqubit Entanglement by Algebraic Geometry
• An Algebraic-Geometric Characterization of Tripartite Entanglement
• Classification of four qubit states and their stabilisers under SLOCC operations
• Classification and Quantification of Entanglement Through Wedge Product and Geometry
• Geometric genuine multipartite entanglement for four-qubit systems
• Classifying Entanglement by Algebraic Geometry
• Special core tensors of multi-qubit states and the concurrency of three lines