Three qubits can be entangled in two inequivalent ways

Three qubits can be entangled in two inequivalent ways

February 1, 2008 | W. Dür, G. Vidal and J. I. Cirac
This paper investigates the classification of entangled states under stochastic local operations and classical communication (SLOCC). It shows that for three-qubit systems, there are two inequivalent types of genuine tripartite entanglement: the GHZ state and the W state. The GHZ state is maximally entangled, but loses all entanglement when one qubit is traced out. In contrast, the W state retains maximally bipartite entanglement even when one qubit is traced out. The paper also generalizes these results to higher-dimensional and larger multipartite systems, showing that typically, two randomly chosen pure states cannot be converted into each other by means of LOCC. The study highlights the importance of distinguishing between different classes of entangled states and their robustness against particle loss. The 3-tangle, a measure of tripartite entanglement, is shown to be invariant under SLOCC and helps in identifying the two distinct classes of entangled states. The paper concludes that the W state is particularly robust against loss of one qubit and is a key example of a state with maximal bipartite entanglement.This paper investigates the classification of entangled states under stochastic local operations and classical communication (SLOCC). It shows that for three-qubit systems, there are two inequivalent types of genuine tripartite entanglement: the GHZ state and the W state. The GHZ state is maximally entangled, but loses all entanglement when one qubit is traced out. In contrast, the W state retains maximally bipartite entanglement even when one qubit is traced out. The paper also generalizes these results to higher-dimensional and larger multipartite systems, showing that typically, two randomly chosen pure states cannot be converted into each other by means of LOCC. The study highlights the importance of distinguishing between different classes of entangled states and their robustness against particle loss. The 3-tangle, a measure of tripartite entanglement, is shown to be invariant under SLOCC and helps in identifying the two distinct classes of entangled states. The paper concludes that the W state is particularly robust against loss of one qubit and is a key example of a state with maximal bipartite entanglement.
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[slides and audio] Three qubits can be entangled in two inequivalent ways