Four qubits can be entangled in nine different ways

By Frank Verstraete, Jeroen Dehaene, B. De Moor, H. Verschelde. 2001

583 citations recorded by the source corpus.

We consider a single copy of a pure four-partite state of qubits and investigate its behavior under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This leads to a complete classification of all different classes of pure states of four qubits. It is shown that there exist nine families of states corresponding to nine different ways of entangling four qubits. The states in the generic family give rise to Greenberger-Horne-Zeilinger-like entanglement. The other ones contain essentially two-or three-qubit entanglement distributed among the four parties. The concept of concurrence and 3-tangle is generalized to the case of mixed states of four qubits, giving rise to a seven-parameter family of entanglement monotones. Finally, the SLOCC operations maximizing all these entanglement monotones are derived, yielding the optimal single-copy distillation protocol.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/96cdc4f72917c7390b41cf761a0a6f7e7f09d36d

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Entanglement certification from theory to experiment (2018, background): “[227] F.”
Normal forms and entanglement measures for multipartite quantum states (2001, background): “As a last remark, we give an example of a state that is brought into a non-zero normal form by SLOCC operators that are unbounded: |ψ〉 ≃ a(|0000〉+ |1111〉) + |01〉(|10〉+ |01〉) (2) The normal form is just given by the GHZ-state (|0000〉+ |1111〉), but as can be derived from the results presented in [15],”
Entanglement detection (2008, background): “At least a classification via equivalence classes under SLOCC is not simple, since it has been shown that already for four qubits there are infinitely many equivalence classes under SLOCC [194,195].”
Entanglement in many-body systems (2007, background): “…and its quantification are at a preliminary stage even for distinguishable particles (see however Briand et al., 2003, 2004; Dür et al., 2000; Luque and Thibon, 2005; Mandilara et al., 2006; Miyake and Wadati, 2002; Osterloh and Siewert, 2005, 2006; Verstraete et al., 2002 and references therein).”
Genuinely multipartite entangled states and orthogonal arrays (2014, background): “In the case of N = 4 qubits the number of inequivalent classes of pure states grows to nine [4] or more [5], if another classification is used.”