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
The paper by Dür, Vidal, and Cirac explores the entanglement properties of pure states of three qubits under stochastic local operations and classical communication (SLOCC). They define equivalence classes of entangled states based on the ability to convert one state into another with a non-zero probability using SLOCC. This classification reveals two distinct types of genuine tripartite entanglement: the GHZ state and the W state. The GHZ state is maximally entangled, while the W state retains maximally bipartite entanglement when any one of the three qubits is traced out. The authors also show that for multipartite systems with more than three qubits, the set of entangled states is typically inaccessible, meaning that two random pure states are usually not connected by SLOCC. They further analyze the robustness of entanglement in the W state against particle losses, finding that it retains the highest amount of bipartite entanglement. Finally, they generalize their findings to multipartite systems with \( N \) qubits, concluding that there are infinitely many inequivalent kinds of entanglement for \( N \geq 4 \).The paper by Dür, Vidal, and Cirac explores the entanglement properties of pure states of three qubits under stochastic local operations and classical communication (SLOCC). They define equivalence classes of entangled states based on the ability to convert one state into another with a non-zero probability using SLOCC. This classification reveals two distinct types of genuine tripartite entanglement: the GHZ state and the W state. The GHZ state is maximally entangled, while the W state retains maximally bipartite entanglement when any one of the three qubits is traced out. The authors also show that for multipartite systems with more than three qubits, the set of entangled states is typically inaccessible, meaning that two random pure states are usually not connected by SLOCC. They further analyze the robustness of entanglement in the W state against particle losses, finding that it retains the highest amount of bipartite entanglement. Finally, they generalize their findings to multipartite systems with \( N \) qubits, concluding that there are infinitely many inequivalent kinds of entanglement for \( N \geq 4 \).
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