Reference : Multipartite-entanglement monotones and polynomial invariants
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Physics
Multipartite-entanglement monotones and polynomial invariants
Eltschka, Christopher [> >]
Bastin, Thierry mailto [Université de Liège - ULiège > Département de physique > Spectroscopie atomique et Physique des atomes froids >]
Osterloh, Andreas [> >]
Siewert, Jens [> >]
Physical Review A
American Physical Society
Yes (verified by ORBi)
College Park
[en] We show that a positive homogeneous function that is invariant under determinant 1 stochastic local operations and classical communication (SLOCC) transformations defines an N-qubit entanglement monotone if and only if the homogeneous degree is not larger than four. We then describe a common basis and formalism for the N-tangle and other known invariant polynomials of degree four. This allows us to elucidate the relation of the four-qubit invariants defined by Luque and Thibon [Phys. Rev. A 67, 042303 (2003)] and the reduced two-qubit density matrices of the states under consideration, thus giving a physical interpretation for those invariants. We demonstrate that this is a special case of a completely general law that holds for any multipartite system with bipartitions of equal dimension, e.g., for an even number of qudits.
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