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arXiv:quant-ph/0307067 · Physical Review A

Multipartite entanglement in 2×2×n quantum systems

Akimasa Miyake, Frank Verstraete

Published Jan 8, 2004• 69 citations
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Abstract

We classify multipartite entangled states in the Hilbert space $\mathcal{H}={C}^{2}\ensuremath{\bigotimes}{C}^{2}\ensuremath{\bigotimes}{C}^{n}(n>~4),$ for example, the four-qubit system distributed over three parties, under local filtering operations. We show that there exist nine essentially different classes of states, giving rise to a five-graded partially ordered structure, including the celebrated Greenberger-Horne-Zeilinger and W classes of three qubits. In particular, all $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}n$ states can be deterministically prepared from one maximally entangled state, and some applications such as entanglement swapping are discussed.

DOI
10.1103/physreva.69.012101

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We classify multipartite entangled states in the Hilbert space H=C2\ensuremath⨂C2\ensuremath⨂Cn(n> 4),\mathcal{H}={C}^{2}\ensuremath{\bigotimes}{C}^{2}\ensuremath{\bigotimes}{C}^{n}(n>~4),H=C2\ensuremath⨂C2\ensuremath⨂Cn(n> 4), for example, the four-qubit system distributed over three parties, under local filtering operations. We show that there exist nine essentially different classes of states, giving rise to a five-graded partially ordered structure, including the celebrated Greenberger-Horne-Zeilinger and W classes of three qubits. In particular, all 2\ifmmode×\else\texttimes\fi2\ifmmode×\else\texttimes\fin2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}n2\ifmmode×\else\texttimes\fi2\ifmmode×\else\texttimes\fin states can be deterministically prepared from one maximally entangled state, and some applications such as entanglement swapping are discussed.
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