An algebraic approach to the study of multipartite entanglement |
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Authors: | S. Di Martino B. Militello A. Messina |
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Affiliation: | 1. Dipartimento di Matematica dell’Università di Bari, Via Orabona 4, 70125, Bari, Italy 2. Dipartimento di Fisica dell’Università di Palermo, Via Archirafi 36, 90123, Palermo, Italy
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Abstract: | We introduce a simple algebraic approach to the study of multipartite entanglement for pure states together with a class of suitable functionals able to detect the entanglement. On this basis, we reproduce some known results. Indeed, by investigating the properties of the introduced functionals, we show that a subset of such class is strictly connected to the purity. Moreover, we provide a direct and basic solution to the problem of simultaneous maximization of three appropriate functionals for three-qubit states, confirming that the simultaneous maximization of the entanglement for all possible bipartitions is compatible only with the structure of the GHZ states. |
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