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Antisymmetric multi-partite quantum states and their applications

Jex, I. and Alber, G. and Barnett, S.M. and Delgado, A. (2003) Antisymmetric multi-partite quantum states and their applications. Progress of Physics, 51 (2). pp. 172-178. ISSN 0015-8208

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Entanglement is a powerful resource for processing quantum information. In this context pure, maximally entangled states have received considerable attention. In the case of bipartite qubit-systems the four orthonormal Bell-states are of this type. One of these Bell states, the singlet Bell-state, has the additional property of being antisymmetric with respect to particle exchange. In this contribution we discuss possible generalizations of this antisymmetric Bell-state to cases with more than two particles and with single-particle Hilbert spaces involving more than two dimensions. We review basic properties of these totally antisymmetric states. Among possible applications of this class of states we analyze a new quantum key sharing protocol and methods for comparing quantum states.